the angle of elevation to a nearby tree from point on the ground is measured to be 55 degrees. a point on the ground is 101 feet from the tree. Refer to the diagram below to answer each question

To solve the problem, we need to find the height of the tree using the given angle of elevation and the distance from the point on the ground to the tree.

Given:

1. The angle of elevation to the top of the tree is 55 degrees.

2. The distance from the point on the ground to the tree is 101 feet.

We can use trigonometry to solve this problem. Specifically, we will use the tangent function, which relates the angle of elevation to the opposite side

height of the tree and the adjacent side distance from the point on the ground to the tree.

The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side:

tanangle = opposite/adjacent

In this case:

tan55degrees = height of the tree / 101 feet

Let h be the height of the tree. Then we have:

tan55degrees = h / 101

To find h, we need to solve for h:

h = 101 * tan55degrees

Using a calculator to find the value of tan55degrees:

tan55degrees ≈ 1.4281

Now, substitute this value back into the equation:

h = 101 * 1.4281

h ≈ 144.2381

Therefore, the height of the tree is approximately 144.24 feet.