How to find the height of an equilateral triangle - Math
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ΔABC is an equilateral triangle with side of length 8.
Find the height (to the nearest tenth).
ΔABC is an equilateral triangle with side of length 8.
Find the height (to the nearest tenth).
Equilateral triangles have sides of equal length, with angles of 60°. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles.
Now, the side of the original equilateral triangle (lets call it "a") is the hypotenuse of the 30-60-90 triangle. Because the 30-60-90 triange is a special triangle, we know that the sides are x, x
, and 2x, respectively.
Thus, a = 2x and x = a/2.
Height of the equilateral triangle = 
Equilateral triangles have sides of equal length, with angles of 60°. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles.
Now, the side of the original equilateral triangle (lets call it "a") is the hypotenuse of the 30-60-90 triangle. Because the 30-60-90 triange is a special triangle, we know that the sides are x, x
Thus, a = 2x and x = a/2.
Height of the equilateral triangle =
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ΔABC is an equilateral triangle with side 12.
Find the height of ΔABC (to the nearest tenth).
ΔABC is an equilateral triangle with side 12.
Find the height of ΔABC (to the nearest tenth).
Equilateral triangles have sides of all equal length and angles of 60°. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles.
Now, the side of the original equilateral triangle (lets call it "a") is the hypotenuse of the 30-60-90 triangle. Because the 30-60-90 triange is a special triangle, we know that the sides are x, x
, and 2x, respectively.
Thus, a = 2x and x = a/2.
Height of the equilateral triangle = 
Equilateral triangles have sides of all equal length and angles of 60°. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles.
Now, the side of the original equilateral triangle (lets call it "a") is the hypotenuse of the 30-60-90 triangle. Because the 30-60-90 triange is a special triangle, we know that the sides are x, x
Thus, a = 2x and x = a/2.
Height of the equilateral triangle =
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What is the height of an equilateral triangle with a side length of 8 in?
What is the height of an equilateral triangle with a side length of 8 in?
An equilateral triangle has three congruent sides, and is also an equiangular triangle with three congruent angles that each meansure 60 degrees.
To find the height we divide the triangle into two special 30 - 60 - 90 right triangles by drawing a line from one corner to the center of the opposite side. This segment will be the height, and will be opposite from one of the 60 degree angles and adjacent to a 30 degree angle. The special right triangle gives side ratios of 
, 
, and 
. The hypoteneuse, the side opposite the 90 degree angle, is the full length of one side of the triangle and is equal to 
. Using this information, we can find the lengths of each side fo the special triangle.
The side with length 
will be the height (opposite the 60 degree angle). The height is 
inches.
An equilateral triangle has three congruent sides, and is also an equiangular triangle with three congruent angles that each meansure 60 degrees.
To find the height we divide the triangle into two special 30 - 60 - 90 right triangles by drawing a line from one corner to the center of the opposite side. This segment will be the height, and will be opposite from one of the 60 degree angles and adjacent to a 30 degree angle. The special right triangle gives side ratios of
The side with length
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Find the height of an equilateral triangle with a side length of 
. Round your answer to the nearest tenth.
Find the height of an equilateral triangle with a side length of
An equilateral triangle has three equal sides, as can be deduced from its name. This also means that as a result, the triangle is also equiangular. That is, all its interior angles are the same. Because the sum of internal angles of a triangle is 
, that means that each interior angle is 
.
The height (the dotted line in the diagram) is the length that bisects the apical angle while bisecting the base of the triangle. Drawing the dotted line splits the equilateral triangle into two congruent right triangles. Because they're the same, we only need to consider one of the two smaller triangles to obtain our answer. Keeping in mind that the base of the equilateral triangle has been bisected, this means that the base of the right triangle has the length of 
. With a base of 
and a hypotenuse of 
, we can easily solve for the height (the third side) with the Pythagorean Theorem.
This problem can also be solved using trigonometric functions or even revisiting 30-60-90 triangle rules.
Using the Pythagorean Theorem,
Therefore, the height of the equilateral triangle is 
.
An equilateral triangle has three equal sides, as can be deduced from its name. This also means that as a result, the triangle is also equiangular. That is, all its interior angles are the same. Because the sum of internal angles of a triangle is
The height (the dotted line in the diagram) is the length that bisects the apical angle while bisecting the base of the triangle. Drawing the dotted line splits the equilateral triangle into two congruent right triangles. Because they're the same, we only need to consider one of the two smaller triangles to obtain our answer. Keeping in mind that the base of the equilateral triangle has been bisected, this means that the base of the right triangle has the length of
This problem can also be solved using trigonometric functions or even revisiting 30-60-90 triangle rules.
Using the Pythagorean Theorem,
Therefore, the height of the equilateral triangle is
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What is the height of a triangle with side lengths 4, 4, 4?
What is the height of a triangle with side lengths 4, 4, 4?
To solve, it's easiest to first visualize the height's relationship with the rest of the triangle's sides:
The height is one of the legs of a right triangle. The hypotenuse is 4, and the other leg is 2, or half of the base side, 4. To determine the height, use Pythagorean Theorem:
subtract 4 from both sides
take the square root of both sides
To solve, it's easiest to first visualize the height's relationship with the rest of the triangle's sides:
The height is one of the legs of a right triangle. The hypotenuse is 4, and the other leg is 2, or half of the base side, 4. To determine the height, use Pythagorean Theorem:
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If an equilateral triangle has a length of 
for all sides, what would be the heigh of the triangle? Round to the nearest tenth.
If an equilateral triangle has a length of
The following formula can be used to determine the height of an equilateral triangle when we are given the length of the sides:
The following formula can be used to determine the height of an equilateral triangle when we are given the length of the sides:
Compare your answer with the correct one above
The equilateral triangle shown below has a side length of 
. Given this information, solve for the height of the triangle.
The equilateral triangle shown below has a side length of
To solve for the height of an equilateral triangle, we can divide the triangle into two right triangles. In the below image, the bisecting line represents the height, and we can solve for height by applying the Pythagorean Theorem:
To solve for the height of an equilateral triangle, we can divide the triangle into two right triangles. In the below image, the bisecting line represents the height, and we can solve for height by applying the Pythagorean Theorem:
Compare your answer with the correct one above
What is the height of an equilateral triangle with a side length of 8 in?
What is the height of an equilateral triangle with a side length of 8 in?
An equilateral triangle has three congruent sides, and is also an equiangular triangle with three congruent angles that each meansure 60 degrees.
To find the height we divide the triangle into two special 30 - 60 - 90 right triangles by drawing a line from one corner to the center of the opposite side. This segment will be the height, and will be opposite from one of the 60 degree angles and adjacent to a 30 degree angle. The special right triangle gives side ratios of , , and . The hypoteneuse, the side opposite the 90 degree angle, is the full length of one side of the triangle and is equal to . Using this information, we can find the lengths of each side fo the special triangle.
The side with length will be the height (opposite the 60 degree angle). The height is inches.
An equilateral triangle has three congruent sides, and is also an equiangular triangle with three congruent angles that each meansure 60 degrees.
To find the height we divide the triangle into two special 30 - 60 - 90 right triangles by drawing a line from one corner to the center of the opposite side. This segment will be the height, and will be opposite from one of the 60 degree angles and adjacent to a 30 degree angle. The special right triangle gives side ratios of
The side with length
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An equilateral triangle has a side length of 
. What is the triangle's height 
?
An equilateral triangle has a side length of
The altitude, 
, divides the equilateral triangle into two 
right triangles and divides the bottom side in half.
In a 
right triangle, the sides of the triangle equal 
, 
, and 
. In these equations 
equals the length of the smallest side, which in our triangle is 
or 
.
In this scenario:
and
Therefore,
The altitude,
In a
In this scenario:
and
Therefore,
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What is the height of an equilateral triangle with side 6?
What is the height of an equilateral triangle with side 6?
When you draw the height in an equilateral triangle, it makes two 30-60-90 triangles. Because of that relationship, the height (which is across from the 
) is 
.
When you draw the height in an equilateral triangle, it makes two 30-60-90 triangles. Because of that relationship, the height (which is across from the
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An equilateral triangle has a side length of 
. What is its height, 
?
An equilateral triangle has a side length of
An altitude slices an equilateral triangle into two 
triangles. These triangles follow a side-length pattern. The smallest of the two legs equals 
and the hypotenuse equals 
. By way of the Pythagorean Theorem, the longest leg or 
.
Therefore, we can find the height of the altitude of this triangle by designating a value to 
. The hypotenuse of one of the 
is also the side of the original equilateral triangle. Therefore, one can say that 
and 
.
An altitude slices an equilateral triangle into two
Therefore, we can find the height of the altitude of this triangle by designating a value to
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Find the height of the following equilateral triangle:
Find the height of the following equilateral triangle:
Each angle in an equilateral triangle is 
.
Use the formula for 
triangles in order to find the length of the height.
The formula is:
Where 
is the length of the side opposite the 
If we were to create a 
triangle by drawing the height, the length of the side is 
, the base is 
, and the height is 
.
Each angle in an equilateral triangle is
Use the formula for
The formula is:
Where
If we were to create a
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Solve for the value of X in the following equilateral triangle:
Solve for the value of X in the following equilateral triangle:
If we draw a line segment between X and the base of the triangle, we form a 
triangle.
We can use the relationships between the sides of a 
triangle in order to find the length of X.
We know the base opposite the 
is 
.
The value of the height opposite the 
must then be 
, or 
.
Therefore, the value of X will be twice the value of the height:
If we draw a line segment between X and the base of the triangle, we form a
We can use the relationships between the sides of a
We know the base opposite the
The value of the height opposite the
Therefore, the value of X will be twice the value of the height:
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ΔABC is an equilateral triangle with side of length 8.
Find the height (to the nearest tenth).
ΔABC is an equilateral triangle with side of length 8.
Find the height (to the nearest tenth).
Equilateral triangles have sides of equal length, with angles of 60°. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles.
Now, the side of the original equilateral triangle (lets call it "a") is the hypotenuse of the 30-60-90 triangle. Because the 30-60-90 triange is a special triangle, we know that the sides are x, x, and 2x, respectively.
Thus, a = 2x and x = a/2.
Height of the equilateral triangle =
Equilateral triangles have sides of equal length, with angles of 60°. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles.
Now, the side of the original equilateral triangle (lets call it "a") is the hypotenuse of the 30-60-90 triangle. Because the 30-60-90 triange is a special triangle, we know that the sides are x, x
Thus, a = 2x and x = a/2.
Height of the equilateral triangle =
Compare your answer with the correct one above
ΔABC is an equilateral triangle with side 12.
Find the height of ΔABC (to the nearest tenth).
ΔABC is an equilateral triangle with side 12.
Find the height of ΔABC (to the nearest tenth).
Equilateral triangles have sides of all equal length and angles of 60°. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles.
Now, the side of the original equilateral triangle (lets call it "a") is the hypotenuse of the 30-60-90 triangle. Because the 30-60-90 triange is a special triangle, we know that the sides are x, x, and 2x, respectively.
Thus, a = 2x and x = a/2.
Height of the equilateral triangle =
Equilateral triangles have sides of all equal length and angles of 60°. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles.
Now, the side of the original equilateral triangle (lets call it "a") is the hypotenuse of the 30-60-90 triangle. Because the 30-60-90 triange is a special triangle, we know that the sides are x, x
Thus, a = 2x and x = a/2.
Height of the equilateral triangle =
Compare your answer with the correct one above
What is the height of an equilateral triangle with a side length of 8 in?
What is the height of an equilateral triangle with a side length of 8 in?
An equilateral triangle has three congruent sides, and is also an equiangular triangle with three congruent angles that each meansure 60 degrees.
To find the height we divide the triangle into two special 30 - 60 - 90 right triangles by drawing a line from one corner to the center of the opposite side. This segment will be the height, and will be opposite from one of the 60 degree angles and adjacent to a 30 degree angle. The special right triangle gives side ratios of , , and . The hypoteneuse, the side opposite the 90 degree angle, is the full length of one side of the triangle and is equal to . Using this information, we can find the lengths of each side fo the special triangle.
The side with length will be the height (opposite the 60 degree angle). The height is inches.
An equilateral triangle has three congruent sides, and is also an equiangular triangle with three congruent angles that each meansure 60 degrees.
To find the height we divide the triangle into two special 30 - 60 - 90 right triangles by drawing a line from one corner to the center of the opposite side. This segment will be the height, and will be opposite from one of the 60 degree angles and adjacent to a 30 degree angle. The special right triangle gives side ratios of
The side with length
Compare your answer with the correct one above
Find the height of an equilateral triangle with a side length of . Round your answer to the nearest tenth.
Find the height of an equilateral triangle with a side length of
An equilateral triangle has three equal sides, as can be deduced from its name. This also means that as a result, the triangle is also equiangular. That is, all its interior angles are the same. Because the sum of internal angles of a triangle is , that means that each interior angle is .
The height (the dotted line in the diagram) is the length that bisects the apical angle while bisecting the base of the triangle. Drawing the dotted line splits the equilateral triangle into two congruent right triangles. Because they're the same, we only need to consider one of the two smaller triangles to obtain our answer. Keeping in mind that the base of the equilateral triangle has been bisected, this means that the base of the right triangle has the length of . With a base of and a hypotenuse of , we can easily solve for the height (the third side) with the Pythagorean Theorem.
This problem can also be solved using trigonometric functions or even revisiting 30-60-90 triangle rules.
Using the Pythagorean Theorem,
Therefore, the height of the equilateral triangle is .
An equilateral triangle has three equal sides, as can be deduced from its name. This also means that as a result, the triangle is also equiangular. That is, all its interior angles are the same. Because the sum of internal angles of a triangle is
The height (the dotted line in the diagram) is the length that bisects the apical angle while bisecting the base of the triangle. Drawing the dotted line splits the equilateral triangle into two congruent right triangles. Because they're the same, we only need to consider one of the two smaller triangles to obtain our answer. Keeping in mind that the base of the equilateral triangle has been bisected, this means that the base of the right triangle has the length of
This problem can also be solved using trigonometric functions or even revisiting 30-60-90 triangle rules.
Using the Pythagorean Theorem,
Therefore, the height of the equilateral triangle is
Compare your answer with the correct one above
What is the height of a triangle with side lengths 4, 4, 4?
What is the height of a triangle with side lengths 4, 4, 4?
To solve, it's easiest to first visualize the height's relationship with the rest of the triangle's sides:
The height is one of the legs of a right triangle. The hypotenuse is 4, and the other leg is 2, or half of the base side, 4. To determine the height, use Pythagorean Theorem:
subtract 4 from both sides
take the square root of both sides
To solve, it's easiest to first visualize the height's relationship with the rest of the triangle's sides:
The height is one of the legs of a right triangle. The hypotenuse is 4, and the other leg is 2, or half of the base side, 4. To determine the height, use Pythagorean Theorem:
Compare your answer with the correct one above
If an equilateral triangle has a length of for all sides, what would be the heigh of the triangle? Round to the nearest tenth.
If an equilateral triangle has a length of
The following formula can be used to determine the height of an equilateral triangle when we are given the length of the sides:
The following formula can be used to determine the height of an equilateral triangle when we are given the length of the sides:
Compare your answer with the correct one above
The equilateral triangle shown below has a side length of . Given this information, solve for the height of the triangle.
The equilateral triangle shown below has a side length of
To solve for the height of an equilateral triangle, we can divide the triangle into two right triangles. In the below image, the bisecting line represents the height, and we can solve for height by applying the Pythagorean Theorem:
To solve for the height of an equilateral triangle, we can divide the triangle into two right triangles. In the below image, the bisecting line represents the height, and we can solve for height by applying the Pythagorean Theorem:
Compare your answer with the correct one above