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mart [117]
3 years ago
9

The angle of depression from the top of a cruise ship to the top of a sailboat is 22. Sitting above water, the cruise ship is 23

6 feet tall while the sailboat is 27 feet tall. Find the distance between the cruise ship and the sailboat.

Mathematics
1 answer:
dusya [7]3 years ago
3 0

Answer:

The distance between the cruise ship and the sail boat is 517 feet.

Step-by-step explanation:

The cruise ship is 236 feet tall, and the sailboat is 236 tall; this means the distance between the top of the cruise ship and the top of the sail boat is

236 feet - 27 feet = 209 feet.

We also know that the angel of depression from the top of the cruise ship to the bottom of the cruise ship is 22°. This forms a right triangle as shown in the figure attached.

Now from trigonometry we get:

tan \: \theta = \dfrac{209}{d}

d= \dfrac{209}{tan\:\theta }

\boxed{d=517ft}

The distance between the cruise ship and the sailboat is 517 feet.

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