Question

A man standing on a lighthouse of height 162 ft sights two boats directly in front of him. One is at an angle of depression of 50°, and the other is at an angle of depression of 45°. Identify the distance between the two boats rounded to the nearest foot.

a. 125ft.
b. 191ft.
c. 66ft.

Answer 1

26 ft

Explanation:

Answer 2

d. 26 ft

Explanation:

The mnemonic SOH CAH TOA reminds you of the relation between angles and legs of a right triangle. Here, the lighthouse height is one leg of a right triangle, and the distance from the base of the lighthouse to the boat is the other leg. The relation ...

Tan = Opposite/Adjacent

can be helpful here. It will tell you ...

tan(angle of depression) = (height of lighthouse)/(distance to boat)

Solving for the distance to the boat, we get ...

distance to boat = (height of lighthouse)/tan(angle of depression)

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Then the distance to the first boat is ...

d1 = (162 ft)/tan(50°) ≈ 135.93 ft

and the distance to the second boat is ...

d2 = (162 ft)/tan(45°) = 162 ft

So, the distance between the boats is ...

162.00 ft -135.93 ft = 26.07 ft ≈ 26 ft

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The attached drawing is to scale.