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.

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.

alexismonkey96 alexismonkey96 · Answer 2 · 2020-09-10T18:31:53+02:00

alexismonkey96 alexismonkey96

10-09-2020

Answer:

26 ft

Step-by-step explanation:

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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.

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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.