A cliff on the bank of a river 87 m high. A boat on the river is 22 m away from the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.
A
76\(^o\)
B
64\(^o\)
C
36\(^o\)
D
24\(^o\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
From the figure above, using SOH CAH TOA
Tan\(\alpha\) = \(\frac{\text{opposite}}{\text{adjacent}}\)
Tan\(\alpha\) = \(\frac{87}{22}\) = 3.9545
\(\alpha\) = Tan\(^{-1}\)(3.9545) = 76º
Source: Myschool Past Questions Archive (Record #71874)