Question

A truck parked on the street is 56 m from the base of the apartment building on the right. The angle of elevation from the truck to the top of the building is 40°. The parked truck is 49 m from the base of the apartment building on the left. The angle of elevation from the truck to the top of that building is 50°. Which building is taller?

Answer 1

The taller building is the second building which is the apartment building on the left with an height of 58.4m

Explanation:

This is a Trigonometric question. We solve this using the Tangent formula

tan θ = Opposite side/Adjacent side

We are given 2 buildings

Building 1

tan θ = Opposite side/Adjacent side

θ = Angle of Elevation = 40°

Distance from the base of the building = Adjacent = 56m

Height of the building = Opposite side = unknown

tan 40 = 0pposite/56m

Opposite = tan 40 × 56m

Opposite = 46.989579346m

Approximately = 47m

Height of Building 1 = 47m

Building 2

tan θ = Opposite side/Adjacent side

θ = Angle of Elevation = 50°

Distance from the base of the building = Adjacent = 49m

Height of the building = Opposite side = unknown

tan 50 = 0pposite/49m

Opposite = tan 50 × 49m

Opposite = 58.395926037m

Approximately = 58.4m

Height of Building 2 = 58.4m

The taller building is the second building which is the apartment building on the left with an height of 58.4m