Question

The height to the base of an isosceles triangle is 12.4m, and its base is 40.6m. What are the measurement of the angles of the triangle and the length of its legs?

*m is meters

Answer 1

angles: 31.42°, 31.42°, 117.16°

legs: 23.79 m

Answer 2

• angles: 31.42°, 31.42°, 117.16°
• legs: 23.79 m

Explanation:

The base angles can be found from the definition of the tangent function:

tan(base angle) = height/(half-base length)

base angle = arctan(12.4/20.3) ≈ 31.418°

Then the apex angle is double the complement of this:

apex angle = 2(90° -31.418°) ≈ 117.164°

The base angles are 31.42°, and the apex angle is 117.16°.

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The leg lengths can be computed from the Pythagorean theorem applied to the altitude and the half-base length.

leg length = √(12.4² +20.3²) = √565.85 ≈ 23.789 . . . . meters

The length of the legs is about 23.79 m.