A parasailer is attached to a boat with a rope of length 300 feet. The angle of depression from the parasailer to the boat is 25 degrees. We need to find the height of the parasailer above the boat and round the answer to the nearest tenth of a foot.

1. Problem Description

A parasailer is attached to a boat with a rope of length 300 feet. The angle of depression from the parasailer to the boat is 25 degrees. We need to find the height of the parasailer above the boat and round the answer to the nearest tenth of a foot.

2. Solution Steps

The height above the boat, the rope length, and the angle of depression form a right triangle. Let $h$ be the height of the parasailer above the boat. The angle of depression is equal to the angle of elevation from the boat to the parasailer.

We can use the sine function to relate the angle, the height, and the rope length:

$sin(\theta) = \frac{opposite}{hypotenuse}$

Here, $\theta = 25^\circ$, the opposite side is the height $h$, and the hypotenuse is the rope length, which is 300 feet. So, we have:

$sin(25^\circ) = \frac{h}{300}$

To find the height $h$, we multiply both sides of the equation by 300:

$h = 300 \cdot sin(25^\circ)$

Using a calculator, we find that $sin(25^\circ) \approx 0.4226$. Therefore,

$h = 300 \cdot 0.4226 \approx 126.78$

Rounding to the nearest tenth of a foot, we get $h \approx 126.8$ feet.

3. Final Answer

126.8 ft