Question

a kite flying in the air has a 79 - ft string attached to it, and the string is pulled taut. the angle of elevation of the kite is 50°. find the height of the kite. round your answer to the nearest tenth.

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle where the hypotenuse \(c = 79\) ft and the angle of elevation \(\theta=50^{\circ}\). We want to find the height \(h\) (opposite side to the angle \(\theta\)). The sine ratio is given by \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Substitute the values into the sine formula

Substitute \(\theta = 50^{\circ}\) and \(c = 79\) into \(\sin\theta=\frac{h}{c}\). So, \(h = c\times\sin\theta\).

Step3: Calculate the value

We know that \(\sin(50^{\circ})\approx0.766\). Then \(h=79\times\sin(50^{\circ})\).

$$h = 79\times0.766=60.514$$

Answer:

\(60.5\) ft