A kite is flying at an angle of elevation of about 40 degrees. All 80 meters of string have been let out. Ignoring the sag in the string, find the height of the kite nearest ten meters.
To find the height of the kite, we can use the trigonometric function tangent (tan). The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle.
In this scenario, the angle of elevation is 40 degrees, and the length of the string is the adjacent side. We need to find the height of the kite, which is the opposite side.
Let's consider the right triangle formed by the kite, the string, and the height of the kite. The length of the string is the hypotenuse of the right triangle.
Using the trigonometric identity, we can write:
Tan(angle) = opposite/adjacent
Or
Tan(40°) = height/80
To isolate the height, we can rearrange the equation:
height = tan(40°) * 80
To find the value of the height, we can use a scientific calculator to calculate the tangent of 40 degrees and then multiply it by 80.