Question

The angle of elevation to a nearby tree from a point on the ground is measured to be 54°. How tall is the tree if the point on the ground is 52 feet from the tree?

Answer 1

To determine the height of the tree, we can use trigonometry. The angle of elevation and the distance from the tree to the point on the ground form a right triangle. The height of the tree corresponds to the side opposite the angle of elevation.

Using the trigonometric function tangent (tan), we can set up the following equation:

tan(54°) = height of the tree / distance from the tree

Let's calculate the height of the tree:

tan(54°) = height of the tree / 52 feet

To solve for the height of the tree, we can multiply both sides of the equation by 52:

height of the tree = tan(54°) * 52 feet

Using a scientific calculator, we can evaluate the tangent of 54°:

tan(54°) ≈ 1.37638192047

Therefore, the height of the tree is approximately:

height of the tree ≈ 1.37638192047 * 52 feet

Calculating this value, we find that the approximate height of the tree is:

height of the tree ≈ 71.52 feet

Therefore, the tree is approximately 71.52 feet tall.

I hope this helps! :)

Answer 2

To find the height of the tree, we can use trigonometry. Let's denote the height of the tree as 'h'.

In a right triangle formed by the tree, the point on the ground, and a line connecting them, the angle of elevation (θ) is the angle between the ground and the line of sight to the top of the tree. The opposite side of this angle is the height of the tree (h), and the adjacent side is the distance from the point on the ground to the tree (52 feet).

Using the trigonometric function tangent (tan), we can set up the following equation:

tan(θ) = opposite/adjacent
tan(54°) = h/52

Now we can solve for h:

h = tan(54°) * 52

Using a calculator, we can find the value of tan(54°) ≈ 1.376381920471173.

h ≈ 1.376381920471173 * 52 ≈ 71.551 feet

Therefore, the height of the tree is approximately 71.551 feet.