Question

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

Answer 1

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.

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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