The angle of depression from the top of a lighthouse to a boat in the water is 30°. If the lighthouse is 89 feet tall how far is
the boat from the lighthouse to the nearest foot?
A) 45 feet
B) 51 feet
C) 63 feet
D) 154 feet
1 answer:
Answer:
D) 154 feet
Step-by-step explanation:
The angle is less than 45°, so you know the distance will be more than 89 feet. There is only one choice in that range.
_____
The mnemonic SOH CAH TOA reminds you ...
... Tan = Opposite/Adjacent
so ...
... tan(30°) = (89 ft)/(distance to boat)
Then ...
... distance to boat = (89 ft)/tan(30°) ≈ 154 ft
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