Question

A parasailer is attached to a boat with a rope. While parasailing the angle of depression to the boat is 25º. When the parasailer is attached to the boat with a 300-foot rope, how high above the boat is he? Round your answer to the nearest tenth of a foot a about 2719 ft c. about 177.5 ft b. about 82.8 ft d about 126.8 ft ОА OD

Answer 1

Given:

Angle of depression = 25

300-foot rope

To solve this problem, we will first illustrate the given problem for us to understand how are we going to solve this problem

Here, we are looking for h, or the height between the boat and the parasailer.

To do this, we must be familiar with the trigonometric functions sine, cosine, and tangent first.

`\sin \theta=(opposite)/(hypotenuse)`
`\cos \theta=(adjacent)/(hypotenuse)`
`\tan \theta=(opposite)/(adjacent)`

Where:

opposite is the opposite side of the given angle

adjacent is the side adjacent to the given angle

hypotenuse is the longest side of the right triangle

In this case,

From this, we can rewrite the given as:

angle = 25

hypotenuse = 300

Find adjacent side h.

As we have mentioned earlier,

`\cos \theta=(adjacent)/(hypotenuse)`

Plugging in the given data

`\cos 25=(h)/(300)`

*Multiply both sides by 300

`300\cos 25=h`
`h=271.89`

Since we are asked to round off the answer to its nearest tenth, the final answer would be

`h\approx271.9ft`