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

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #4 : Trigonometric Applications

Isoscelestriangle_800

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

Possible Answers:

Correct answer:

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 ?

Possible Answers:

Correct answer:

Explanation:

Isos

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 #5 : Trigonometric Applications

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

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Possible Answers:

Correct answer:

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: 

 

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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 #10 : Solving Right Triangles

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

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Possible Answers:

Correct answer:

Explanation:

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

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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:

Varsity log graph

Possible Answers:

Correct answer:

Explanation:

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

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

Find the area of the given isosceles triangle:

Varsity log graph

Possible Answers:

Correct answer:

Explanation:

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

Varsity log graph

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:

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