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°. how high off the ground is the kite?

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 52^{\circ}\), the hypotenuse is the length of the string \(100\) feet, and the opposite side is the height \(x\) of the kite off the ground. 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:

\(78.8\) feet