Question

a kite is flying 79 ft off the ground, and its string is pulled taut. the angle of elevation of the kite is 58°. find the length of the string. round your answer to the nearest tenth.

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the height of the kite (opposite side to the angle of elevation) is 79 ft and the angle of elevation is 58°. Let the length of the string be \(l\) (hypotenuse). We use the sine function since \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(58^{\circ})=\frac{79}{l}\).

Step2: Solve for \(l\)

We can rewrite the equation as \(l = \frac{79}{\sin(58^{\circ})}\). We know that \(\sin(58^{\circ})\approx0.848\). Then \(l=\frac{79}{0.848}\approx93.2\).

Answer:

93.2 ft