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:       Explanation:

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: All Precalculus Resources 