Question

Luis is flying a kite, holding his hands a distance of 3.75 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 35^{\circ} ∘. If the string from the kite to his hand is 140 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answer 1

84.1

Explanation:

84.1

Answer 2

To solve this problem, we need to use the tangent function. The tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle. In this problem, the opposite side is the height of the kite above the ground and the adjacent side is the distance between Luis's hands and the kite.

Using the tangent function, we can write:

tan(35) = opposite side / adjacent side

We can use the value of the adjacent side (3.75 feet) and the measure of the angle of elevation to find the value of the opposite side (the height of the kite above the ground).

tan(35) = opposite side / 3.75

We can find the opposite side by multiplying both sides of the equation by 3.75:

opposite side = 3.75 * tan(35)

Using a calculator to find the value of tan(35), we get:

opposite side = 3.75 * 0.7006 = 2.6295 feet

The kite is 2.6295 feet above the ground.

Explanation: