Matthew parks his car between Karen’s and Patrick’s apartment buildings. The car is 46 m in front of Karen’s apartment building. The angle of elevation from the car to the top of the building is 40°. Matthew’s car is 39 m away from Patrick’s apartment building. The angle of elevation from the car to the top of the building is 50°.

Question

a) Determine the height of each building, to the nearest metre.
b) State which building is taller, and by how much.

Answer 1

if the buildings are of height k and p,

k/46 = tan40°
p/39 = tan50°

now just evaluate k and p, take the difference

Answer 2

Take the tangent of Karen’s and Matthew’s building to determine the height. Then subtract the two heights