Question

A kite is flying 70 feet above the ground and is attached to a string tied to a stake on the ground. The angle of elevation formed by the string and the ground is 40°. Find the length of the string to the nearest foot.

Answer 1

taking the length of the string to be the hypothenuse and the vertical height above the ground to be the 'opposite' side,
the length of the string
= 70/sin(40°)
= 109 feet

Answer 2

94 feet.

Explanation:

The angle of elevation is the angle made by the eye of the observer and the ground level. In this instance, it is the angle formed by the string and the ground which is 40°.

From the attached diagram, the length of the string is x and the height above the ground is 70 feet. These two sides are the hypotenuse and the opposite sides respectively

Using SOH CAH TOA

Sin 40 = 70/x

x = 70/sin 40

x = 93.95 feet.

The length of the string to the nearest foot is 94 feet.