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?

Answer 1

Base Angles=31.42°

Length of legs=23.79 m

Vertex angle=117.16°

Explanation:

An isosceles triangle is a triangle whose leg lengths are equal. They also form base angles that are equal.

1. Base angles

Base angles can be solved by using the tan of one of the base angles, let the base angle be ∅.

Using the formula Tan∅=opposite/adjacent

Where the opposite side=Height=12.4 m, and the adjacent side=0.5×Base length= 0.5×40.6=20.3 m

Tan∅=12.4/20.3=0.61

∅=(Tan∧-1)×0.61=31.42°

Base angle=31.42°

2. Length of legs

The length of each of the legs can be g the formula

Hypotenuse=√((Height)²+(0.5×base length)²)=√(12.4²+20.3²)=23.79 m

Length of the legs=23.79 m

3. Vertex angle

Let the vertex angle be x

Total angles in a triangle should add up to 180°, meaning

(2×base angle)+vertex angle=180°

(2×31.42°)+x=180°

62.84+x=180

x=180-62.84=117.16°

Vertex angle=117.16°