Question

a man is standing on the coridor of an 8-storey building and looking down on a tall tree in front of the building. he sees the top of the tree at an angle of depression of 30degrees. if the tree is 160m tall and the man's eyes are 240m above the ground, calculate the angle of depression of the foot of th tree as seen by the man according to maths

Answer 1

Let d be the horizontal distance from the man to the tree. The vertical drop from the man's eyes (240 m) to the tree top (160 m) is 80 m. With angle of depression 30° to the top,

tan 30° = 80 / d ⇒ d = 80 / tan 30° = 80√3.

The vertical drop to the foot is 240 m, so the angle of depression θ to the foot satisfies

tan θ = 240 / d = 240 / (80√3) = √3 ⇒ θ = arctan(√3) = 60°.

Answer: 60°.