Question

You are flying a kite while standing 80 ft from a

fence. If the kite string makes a 50° angle with
the ground, how much string, in feet, is let out
when the kite is directly above the fence?

Answer 1

124.5 ft

Explanation:

Draw a figure. It is a triangle.

Kite

B | \

| \

| \

| \ string

| \

| \

| \

| \

| __ 50 deg \

C |----|---------------------------------------- A

fence 80 ft you are here

You are at point A. The kite is at point B. The fence is at point C. Angle C is a right angle.

The length of the string is the hypotenuse of the triangle, side AB. The bottom side of the triangle, side AC, the ground, is the adjacent leg for angle A.

The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.

`\cos A = (adj)/(hyp)`

`\cos 50^\circ = (AC)/(AB)`

`\cos 50^\circ = (80)/(AB)`

`AB \cos 50^\circ = 80`

`AB = (80)/(\cos 50^\circ)`

`AB = 124.5`

Answer: 124.5 ft