A man is standing in the corridor of a 10-storey building and looking down at…

A man is standing in the corridor of a 10-storey building and looking down at a tall tree in front of the building. He sees the top of the tree at angle of depression of 30^o. If the tree is 200m tall and the man’s eyes are 300m above the ground, calculate the angle of depression of the foot tree as seen by the man

Correct Answer: Option B

Explanation

Let x rep. the angle of depression of the foot of the tree.
tan 30^o = (frac{y}{100})
y = 100 tan 30^o
= 57.8
By Pythagoras, AC² = 300² + 58²
= 900 + 3354
tan x = (frac{opp}{adj})
= (frac{58}{300})
= 0.19
tan x = 0.19
x = tan 0.19
= 60^o