Question

Hudson (3 3 feet tall) is on the beach flying a kite. His angle of elevation looking up to the kite is 40∘ 40 ∘ . The kite string is 125 125 ft long. How high is the kite off the ground?

Answer 1

Answer:

83.35 feet above ground.

Step-by-step explanation:

Please find the attachment.

We have been given that Hudson (3 feet tall) is on the beach flying a kite. His angle of elevation looking up to the kite is 40 degrees. The kite string is 125 ft long.  

We can see that the string of kite forms a right triangle with an angle of elevation (40 degrees) as shown in the attachment.

To solve for h, we will use sine as sine related opposite side of a right triangle with hypotenuse.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

$\text{sin}(40^{\circ})=\frac{h}{125}$

$h=125\cdot \text{sin}(40^{\circ})$

$h=125\cdot 0.642787609687$

$h=80.348451210875\approx 80.35$

To find the height of kite off the ground, we will add height of Hudson to 80.35 feet as well as he is flying the kite.

$80.35+3=83.35$

Therefore, the kite is approximately 83.35 feet above ground.