Trigonometric Applications - Pre-Calculus

Write the formula for the Pythagorean theorem.

In an isosceles right triangle, both legs of the right triangle are equal.

Substitute the either variable and the known hypotheuse and determine the side length.

This length represents both the base and the height of the triangle. Write the area of a triangle and substitute to solve for the area.

In the diagram, AB is cut in half by the altitude.

From here it easy to use right triangle trigonometry to solve for AC.

Since the angle of the isosceles is , the larger angle of the right triangle formed by is also .

Using , we can find :

.

Then solve for :

.

Simplify: .

Lastly, round and add appropriate units: .

The formula for the area of a triangle is:

We already know what the base is and we can find the height by dividing the isosceles triangle into 2 right triangles:

From there, we can use the Pathegorean Theorem to calculate height:

To find the area, now we just plug these values into the formula:

The first step to solve for area is to divide the isosceles into two right triangles:

From there, we can determine the height and base needed for our area equation

From there, height can be easily determined using the Pathegorean Theorem:

Now both values can be plugged into the Area formula:

The first step is to divide this isosceles triangle into 2 right triangles, making it easier to solve:

The equation for area is

We already know the base, so we need to solve for height to get the area.

Then we plug in all values for the equation:

The first step toward finding the area is to divide this isosceles triangle into two right triangles:

Trigonometric ratios can be used to find both the height and the base, which are needed to calculate area:

With both of those values calculated, we can now calculate the area of the triangle:

C is given as 90°.

A is given as 22.620°

a is given as 5

b is given as 12

Therefore...

All angles of a triangle add up to equal 180°.

Given that:

C=90°

B=45°

a=5

c=

Therefore...

All angles of a triangle add up to 180°.

Write the Pythagorean Theorem.

Substitute the values of the leg and hypotenuse. The hypotenuse is the longest side of the right triangle. Solve for the unknown variable.

Given that ABC is a right triangle, the length of hypotenuse BC is the root of the sum of the squares of the two other sides (in other words, . Since AB is cm long and AC is cm long, we get that , and so .

When you are using Pythagorean Theorem to calculate the missing side of a right triangle, it is crucial that you identify which side is the hypotenuse, in the Pythagorean equation . Here you're told that side AC is the longest of the three sides, so 25 will serve as the length of the hypotenuse and the value of . This allows you to set up the equation:

And then you can perform the calculations on the known values:

Meaning that:

From there you can simplify, arriving at a = 4 times the square root of 34.

Use the Pythagorean Theorem to find the other leg.

The length of the given leg is 3, and the unknown leg is .

Use the area of a triangle formula and solve.

Write the formula for the Pythagorean theorem.

In an isosceles right triangle, both legs of the right triangle are equal.

Substitute the either variable and the known hypotheuse and determine the side length.

This length represents both the base and the height of the triangle. Write the area of a triangle and substitute to solve for the area.

In the diagram, AB is cut in half by the altitude.

From here it easy to use right triangle trigonometry to solve for AC.

Since the angle of the isosceles is , the larger angle of the right triangle formed by is also .

Using , we can find :

.

Then solve for :

.

Simplify: .

Lastly, round and add appropriate units: .

The formula for the area of a triangle is:

We already know what the base is and we can find the height by dividing the isosceles triangle into 2 right triangles:

From there, we can use the Pathegorean Theorem to calculate height:

To find the area, now we just plug these values into the formula:

The first step to solve for area is to divide the isosceles into two right triangles:

From there, we can determine the height and base needed for our area equation

From there, height can be easily determined using the Pathegorean Theorem:

Now both values can be plugged into the Area formula:

The first step is to divide this isosceles triangle into 2 right triangles, making it easier to solve:

The equation for area is

We already know the base, so we need to solve for height to get the area.

Then we plug in all values for the equation: