Question

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

Answer 1

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

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 = (209)/(d)`

`d= (209)/(tan\:\theta )`

`\boxed{d=517ft}`

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