Question

a kite is flying 70 feet above the ground and is attached to a string tied to a stake on the ground. the angle of elevation formed by the string and the ground is 40°. find the length of the string to the nearest foot.
a 45 feet
b 83 feet
c 91 feet
d 100 feet

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the height of the kite (opposite side) is \(h = 70\) feet and we need to find the length of the string (hypotenuse) \(l\). The angle of elevation \(\theta=40^{\circ}\). Using the sine function \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin40^{\circ}=\frac{70}{l}\).

Step2: Solve for \(l\)

Rearrange the formula to \(l=\frac{70}{\sin40^{\circ}}\). We know that \(\sin40^{\circ}\approx0.6428\). Then \(l=\frac{70}{0.6428}\approx109\) (rounded to the nearest whole number).

Answer:

D. 109 feet