Question

Penny is flying a kite that is at the end of 50 ft of string. The kite makes a 55° angle of depression with Penny. If the distance from the ground to Penny's hand is 4 feet, how far above the ground is the kite? Explain the solution to this problem.

Answer 1

45 feet

Step-by-step explanation:

We are required to find the height of the kite above the ground.

• The side opposite angle 55 degrees = x

,

• The length of the hypotenuse = 50 ft

From trigonometric ratios:

`\sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}`

Therefore:

`\begin{gathered} \sin 55\degree=(x)/(50) \\ x=50*\sin 55 \\ x=40.96\text{ ft} \end{gathered}`

Since the distance from the ground to Penny's hand is 4 feet, the height of the kite above the ground will be:

`\begin{gathered} =40.96+4 \\ =44.96ft \\ \approx45ft \end{gathered}`