Question

John wants to measure the height of a tree. He walksexactly 100 feet from the base of the tree and looks up. Theangle from the ground to the top of the tree is 33 degrees . How tall isthe tree?

Answer 1

Answer: 58.5 feet

Explanation:

To find the height of the tree, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.

In this case, the angle is 33 degrees and the adjacent side is the distance from the base of the tree to where John is standing, which is 100 feet. The opposite side is the height of the tree, which we want to find.

So, we can set up the equation: tan(33 degrees) = height of the tree / 100 feet.

To solve for the height of the tree, we can multiply both sides of the equation by 100 feet: height of the tree = tan(33 degrees) * 100 feet.

Now, we can use a calculator to find the tangent of 33 degrees, and then multiply it by 100 feet to get the height of the tree.

height of the tree = tan(33 degrees) * 100 feet.

height of the tree ≈ 58.5 feet.

So, the height of the tree is approximately 58.5 feet.