Question

a kite flying in the air has a 95 - ft string attached to it, and the string is pulled taut. the angle of elevation of the kite is 57°. find the height of the kite. round your answer to the nearest tenth.

Explanation:

Step1: Identify the trig - ratio

We have a right - triangle where the length of the hypotenuse (string length) is 95 ft and we want to find the height (opposite side to the given angle of elevation). We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Set up the equation

Let $h$ be the height of the kite. Given $\theta = 57^{\circ}$ and hypotenuse $c = 95$ ft. So, $\sin(57^{\circ})=\frac{h}{95}$.

Step3: Solve for $h$

We can rewrite the equation as $h = 95\times\sin(57^{\circ})$. Since $\sin(57^{\circ})\approx0.8387$, then $h=95\times0.8387 = 79.6765$ ft.

Step4: Round to the nearest tenth

Rounding 79.6765 to the nearest tenth gives 79.7 ft.

Answer:

79.7 ft