To solve this problem, we can use trigonometry, specifically the tangent of the angle. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side.

Here, the angle of depression is given as 25°. However, in the triangle formed by the parasailer, the boat, and the point directly below the parasailer, the angle we are interested in is the complementary angle to the angle of depression, which is also 25°.

The 300-foot rope is the hypotenuse of the triangle. We want to find the height of the parasailer above the boat, which is the opposite side of the triangle.

So, we set up the equation:

tan(25°) = height / 300 feet

Solving for height gives:

height = tan(25°) * 300 feet

Using a calculator, tan(25°) is approximately 0.4663.

So, height = 0.4663 * 300 feet = 139.89 feet

Rounding to the nearest tenth of a foot gives a height of approximately 139.9 feet. So, the parasailer is about 139.9 feet above the boat.

Question

To solve this problem, we can use trigonometry, specifically the tangent of the angle. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side.

Here, the angle of depression is given as 25°. However, in the triangle formed by the parasailer, the boat, and the point directly below the parasailer, the angle we are interested in is the complementary angle to the angle of depression, which is also 25°.

The 300-foot rope is the hypotenuse of the triangle. We want to find the height of the parasailer above the boat, which is the opposite side of the triangle.

So, we set up the equation:

tan(25°) = height / 300 feet

Solving for height gives:

height = tan(25°) * 300 feet

Using a calculator, tan(25°) is approximately 0.4663.

So, height = 0.4663 * 300 feet = 139.89 feet

Rounding to the nearest tenth of a foot gives a height of approximately 139.9 feet. So, the parasailer is about 139.9 feet above the boat.

Knowee AI · Accepted Answer

To solve this problem, we can use trigonometry, specifically the tangent of the angle. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side.

Here, the angle of depression is given as 25°. However, in the triangle formed by the parasailer, the boat, and the point directly below the parasailer, the angle we are interested in is the complementary angle to the angle of depression, which is also 25°.

The 300-foot rope is the hypotenuse of the triangle. We want to find the height of the parasailer above the boat, which is the opposite side of the triangle.

So, we set up the equation:

tan(25°) = height / 300 feet

Solving for height gives:

height = tan(25°) * 300 feet

Using a calculator, tan(25°) is approximately 0.4663.

So, height = 0.4663 * 300 feet = 139.89 feet

Rounding to the nearest tenth of a foot gives a height of approximately 139.9 feet. So, the parasailer is about 139.9 feet above the boat.

A parasailer is attached to a boat with a rope. While parasailing, the angle of depression to the boat is 25°. 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.

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