Kerry got her kite stuck in the very top of a tree. If she knows that she is standing 50 yards away from the tree and the angle that her kite string makes when held to the ground by her feet is 48 degrees, how tall is the tree?

height/50 = tan48°

take over

To find the height of the tree, we can use basic trigonometry principles. Let's assume that the height of the tree is represented by the variable "h."

First, we need to identify a triangle within this problem. We can visualize a right triangle formed by the height of the tree (h), the distance between Kerry and the tree (50 yards), and the angle between the ground and the kite string (48 degrees).

In a right triangle, the side opposite the angle is known as the "opposite" side, the side next to the angle but not the hypotenuse is known as the "adjacent" side, and the side opposite the right angle is known as the "hypotenuse."

In our case, the height of the tree is the opposite side, the distance between Kerry and the tree is the adjacent side, and the kite string is the hypotenuse.

Now, we can use the trigonometric function called tangent (tan) to solve for the height of the tree:

tan(angle) = opposite / adjacent

Plugging in the given values:
tan(48 degrees) = h / 50 yards

To isolate "h," we can multiply both sides of the equation by 50 yards:

50 yards * tan(48 degrees) = h

Calculating this value using a scientific calculator:

h ≈ 50 yards * tan(48 degrees) ≈ 50 * 1.1106 ≈ 55.53 yards

Therefore, the tree is approximately 55.53 yards tall.