Answer:
≈ 106.5 feet
Explanation:
Let's start by drawing a picture of the situation. Imagine a kite flying in the air, with a string attached to it that is pulled taut (pulled tight so there's no slack). The string is 86 feet long. We want to know how high the kite is in the air, and we know that the angle of elevation of the kite is 53 degrees.
Now, the angle of elevation is the angle between the horizontal (the ground) and the line of sight from the observer (you) to the object (the kite). In this case, you are looking up at the kite, so the line of sight is the string that connects the kite to the ground.
To find the height of the kite, we need to use trigonometry. Specifically, we'll use the tangent function, which relates the opposite side of a right triangle (in this case, the height of the kite) to the adjacent side (in this case, the length of the string) and the angle of elevation.The formula for the tangent function is:
tan(theta) = opposite/adjacent
Where theta is the angle of elevation, opposite is the height of the kite, and adjacent is the length of the string.
We know that the angle of elevation is 53 degrees, and the length of the string is 86 feet. So we can plug those values into the formula and solve for the height of the kite:
tan(53) = opposite/86
opposite = 86 * tan(53)
≈ 106.5
So the height of the kite is approximately 106.5 feet.