Brian's kite is flying at the end of 82 of string. His end of string, is 3 feet off the ground. the angle of elevation of the kite is 55 degrees. What is the height of the kite?

sin55 = Y/82, Y = 82*sin55 = 67.2 Ft., h = 67.2 + 3 = 70.2 Ft.

To find the height of the kite, you can use trigonometry, specifically the tangent function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, the angle of elevation of the kite is 55 degrees, which means that the height of the kite is the opposite side, and the distance from Brian to the kite (82 feet) is the adjacent side.

Using the formula:

tangent(angle) = opposite / adjacent

we can plug in the values:

tangent(55 degrees) = height / 82 feet

Now, we can solve for the height:

height = tangent(55 degrees) * 82 feet

Calculating the tangent of 55 degrees using a scientific calculator or a trigonometric table, we get approximately 1.428.

height = 1.428 * 82 feet

So, the height of the kite is approximately 117.096 feet.