Question

Susan and Jorge stand 38 m apart. From Susan's position, the angle of elevation to the top of Big Ben is 65°. From Jorge's position, the angle of elevation to the top of Big Ben is 49.5°. To the nearest meter, how tall is Big Ben?

Answer 1

98 m

Explanation:

You want the height of Big Ben if angles of elevation are 65° and 49.5° from points 38 m apart.

Tangent

The tangent function relates the angle and the sides of a right triangle:

Tangent = Opposite/Adjacent

Solving for the adjacent side, we have ...

Adjacent = Opposite/Tangent

Application

We have a difference of adjacent sides, and we want to find the opposite side (the height of Big Ben).

distance from Jorge - distance from Susan = 38 m

height/tan(49.5°) -height/tan(65°) = 38 m

height = (38 m)(1/tan(49.5°) -1/tan(65°)) ≈ (38 m)/(1/1.1708 -1/2.1445)

height ≈ (38 m)(0.8541 -0.4663) ≈ 97.995 m

The height of Big Ben is about 98 meters.