Question

1. a kite is flying at the end of a stretched string 150 meters long. the string makes an angle of 27 degrees with the level ground. find the height of the kite. round to the nearest tenth. (see yellow hint below.) 294.4 ft 133.7 ft 68.1 ft 76.4 ft

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the string is the hypotenuse ($c = 150$ ft) and the height of the kite is the side opposite the given angle ($\theta=27^{\circ}$). We use the sine function: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Substitute the values into the sine formula

Let $h$ be the height of the kite. Then $\sin(27^{\circ})=\frac{h}{150}$.

Step3: Solve for $h$

Multiply both sides by 150: $h = 150\times\sin(27^{\circ})$.
Using a calculator, $\sin(27^{\circ})\approx0.454$.
So $h=150\times0.454 = 68.1$ ft.

Answer:

68.1 ft