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

JAMB 1979

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

A. 30^o
B. 60^o
C. 45^o
D. 25^o

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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

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