Question

angle of elevation & depression worksheet (cont.)
find all values to the nearest tenth.

1. a man flies a kite with a 100 foot string. the angle of elevation of the

string is ( 52 ^ { circ } ). how high off the ground is the kite?

Explanation:

Step1: Identify the trigonometric ratio

We know the hypotenuse (string length \(h = 100\) feet) and we want to find the opposite side (\(x\), height of the kite). The sine ratio is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), where \(\theta = 52^{\circ}\). So, \(\sin(52^{\circ})=\frac{x}{100}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(52^{\circ})=\frac{x}{100}\) by \(100\). We get \(x = 100\times\sin(52^{\circ})\). Using a calculator, \(\sin(52^{\circ})\approx0.788\). Then \(x=100\times0.788 = 78.8\)

Answer:

The kite is \(78.8\) feet off the ground.