How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem - ISEE Upper Level Quantitative Reasoning

To solve this problem, we must utilize the Pythagorean Theorom, which states that:

We know that the base is , so we can substitute in for . We also know that the height is , so we can substitute in for .

Next we evaluate the exponents:

Now we add them together:

Then, .

is not a perfect square, so we simply write the square root as .

To solve this problem, we are going to use the Pythagorean Theorom, which states that .

We know that this particular right triangle has a base of , which can be substituted for , and a height of , which can be substituted for . If we rewrite the theorom using these numbers, we get:

Next, we evaluate the expoenents:

Then, .

To solve for , we must find the square root of . Since this is not a perfect square, our answer is simply .

According to the Pythagorean Theorem, the equation for the hypotenuse of a right triangle is . Plugging in the sides, we get . Solving for , we find that the hypotenuse is :

By the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let hypotenuse and side length.

This triangle has two angles of 45 and 90 degrees, so the third angle must measure 45 degrees; this is therefore an isosceles right triangle.

By the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let hypotenuse and , lengths of the other two sides.

Given that a rectangle has all right angles, drawing a diagonal will create a right triangle the legs are each 6 feet and 8 feet.

We know that in a 3-4-5 right triangle, when the legs are 3 feet and 4 feet, the hypotenuse will be 5 feet.

Given that the legs of this triangle are twice as long as those in the 3-4-5 triangle, it follows that the hypotense will also be twice as long.

Thus, the diagonal in through the rectangle creates a 6-8-10 triangle. 10 is therefore the length of the diagonal.

The pythagorean theory should be used to solve this problem.

If the legs of a right triangle are 4 and 5, to find the hypotenuse, the following equation must be used to find the hypotenuse, in which c is equal to the hypotenuse:

At your local university, there is a triangular walking path around a grassy area. If the two legs of the triangle form a ninety degree angle, and are each 30 meters long, what is the length of the hypotenuse of the triangle?

This problem asks us to find the hypotenuse of a right triangle. To do so, we can use Pythagorean Theorem.

Where a and b are the short sides of the triangle, and c is our hypotenuse.

We know a and b are both 30 meters, so plug that in and begin!

Write the formula of the Pythagorean Theorem.

The value of is what we will be solving for.

Substitute the side lengths.

Square root both sides.

The answer is:

By the Pythagorean Theorem, which says . being the hypotenuse, or in this problem.

Simply

To solve this problem, we must utilize the Pythagorean Theorom, which states that:

We know that the base is , so we can substitute in for . We also know that the height is , so we can substitute in for .

Next we evaluate the exponents:

Now we add them together:

Then, .

is not a perfect square, so we simply write the square root as .

To solve this problem, we are going to use the Pythagorean Theorom, which states that .

We know that this particular right triangle has a base of , which can be substituted for , and a height of , which can be substituted for . If we rewrite the theorom using these numbers, we get:

Next, we evaluate the expoenents:

Then, .

To solve for , we must find the square root of . Since this is not a perfect square, our answer is simply .

According to the Pythagorean Theorem, the equation for the hypotenuse of a right triangle is . Plugging in the sides, we get . Solving for , we find that the hypotenuse is :

By the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let hypotenuse and side length.

This triangle has two angles of 45 and 90 degrees, so the third angle must measure 45 degrees; this is therefore an isosceles right triangle.

By the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let hypotenuse and , lengths of the other two sides.

Given that a rectangle has all right angles, drawing a diagonal will create a right triangle the legs are each 6 feet and 8 feet.

We know that in a 3-4-5 right triangle, when the legs are 3 feet and 4 feet, the hypotenuse will be 5 feet.

Given that the legs of this triangle are twice as long as those in the 3-4-5 triangle, it follows that the hypotense will also be twice as long.

Thus, the diagonal in through the rectangle creates a 6-8-10 triangle. 10 is therefore the length of the diagonal.

The pythagorean theory should be used to solve this problem.

If the legs of a right triangle are 4 and 5, to find the hypotenuse, the following equation must be used to find the hypotenuse, in which c is equal to the hypotenuse: