Question

a kite flying in the air has a 78 - ft string attached to it, and the string is pulled taut. the angle of elevation of the kite is 55°. find the height of the kite. round your answer to the nearest tenth.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, we know the hypotenuse \(c = 78\) and the angle \(\theta=55^{\circ}\). We want to find the side opposite the angle \(\theta\). The sine ratio is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Substitute the values into the formula

Let \(h\) be the height (opposite side). Using the formula \(\sin\theta=\frac{h}{c}\), with \(\theta = 55^{\circ}\) and \(c = 78\). So \(h = c\times\sin\theta\).
Since \(\sin(55^{\circ})\approx0.8192\), then \(h=78\times\sin(55^{\circ})\).

Step3: Calculate the value

\(h = 78\times0.8192=63.9\) (rounded to the nearest tenth)

Answer:

\(63.9\)