# Precalculus : Solve an Isosceles Triangle By Dividing Into 2 Right Triangles

## Example Questions

### Example Question #1 : Solve An Isosceles Triangle By Dividing Into 2 Right Triangles

Given , and the lower angles of the isosceles triangle are , what is the length of ? Round to the nearest tenth.

Explanation:

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: .

### Example Question #2 : Solve An Isosceles Triangle By Dividing Into 2 Right Triangles

In isosceles triangle , .  If side , what is the approximate length of the two legs  and ?

Explanation:

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

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

### Example Question #1 : Solve An Isosceles Triangle By Dividing Into 2 Right Triangles

Find the area of the following Isosceles triangle (units are in cm):

Explanation:

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:

### Example Question #2 : Trigonometric Applications

Find the area of the given isosceles triangle and round all values to the nearest tenth:

Explanation:

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:

### Example Question #1 : Solve An Isosceles Triangle By Dividing Into 2 Right Triangles

Find the area of the given isosceles triangle:

Explanation:

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:

### Example Question #12 : Trigonometric Applications

Find the area of the given isosceles triangle: