Question

A 50 ft kite string is flying on the beach above an umbrella. You are holding the end

of the string and are 12 feet from the umbrella. How high in the air is the kite flying?
Round to the nearest degree.

Answer 1

The height of the kite is 48.54 feet

The angle of elevation is 76.11°

Explanation:

To find the height of the kite, we can use the Pythagoras' theorem in the triangle created by the length of the string (hypotenuse), the height of the kite and the distance to the umbrella (catheti).

Then, we have:

50^2 = 12^2 + height^2

height^2 = 2500 - 144

height^2 = 2356

height = 48.54 ft

So the kite is 48.54 feet high in the air.

The angle of elevation can be calculated using the cosine relation:

cos(angle) = 12 / 50

cos(angle) = 0.24

angle = 76.11°