JAMB - Mathematics (1979 - No. 41)
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 30o. 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
30o
60o
45o
25o
הֶסבֵּר
Let x rep. the angle of depression of the foot of the tree.
tan 30o = \(\frac{y}{100}\)
y = 100 tan 30o
= 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
= 60o
tan 30o = \(\frac{y}{100}\)
y = 100 tan 30o
= 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
= 60o