A kite is flying at the end of a straight string that has a length of 250 meters. The string makes an angle of 65 degrees with the ground.

Question

A kite is flying at the end of a straight string that has a length of 250 meters. The string makes an angle of 65 degrees with the ground. How high above the ground is the kite?

Answer 1

Think of a right triangle, with the hypotenuse (the longest side) as the string. You want to know the height, which is the one of the sides of the triangle. The angle with the ground is 65 deg, so the opposite angle (between the string and the height) is 25 deg (90-65=25).

 

Use the trigonometric function cos (cosine) to figure this out. The cosine of 25 deg = adjacent side (height) / hypotenuse (string). So, cos 25 deg = x/250. Find the value of cos 25, then solve for x.

 

.9063 = x/250

 

x = .9063*250 = 226.58

 

The kite is 226.58 meters above the ground.

Answer 2

the length of the kite is the hypotenuse of the right triangle.

 

the height is the opposite side of 65°

 

sin 65 = height/hypotenuse

height = 250sin 65 = 226.58 m