Question

Assuming that a 360-foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be 63°, how far from the base of the tree am I?

Round your answer to four decimal places.

Answer 1

To calculate the distance from the base of the giant redwood tree, we can use trigonometry and the tangent function.

Let's denote the distance from the base of the tree as "x". The height of the tree is given as 360 feet. The angle of elevation from your position to the top of the tree is 63°.

We can set up the following equation:

tangent(63°) = height of the tree (360 ft) / distance from the base (x)

Mathematically, this can be written as:

tan(63°) = 360 ft / x

To find "x," we rearrange the equation:

x = 360 ft / tan(63°)

Using a calculator, we can evaluate this expression:

x ≈ 194.3665 ft

Therefore, you are approximately 194.3665 feet away from the base of the giant redwood tree.