Question

a kite is flying 77 ft off the ground, and its string is pulled taut. the angle of elevation of the kite is 54°. find the nearest tenth.

Explanation:

Step1: Identify the trig - ratio

We have a right - triangle where the height of the kite (opposite side to the angle of elevation) is 77 ft and we want to find the length of the string (hypotenuse). We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 54^{\circ}$ and the opposite side $a = 77$ ft, and the hypotenuse is $x$. So, $\sin(54^{\circ})=\frac{77}{x}$.

Step2: Solve for $x$

We can re - arrange the equation $\sin(54^{\circ})=\frac{77}{x}$ to get $x=\frac{77}{\sin(54^{\circ})}$. We know that $\sin(54^{\circ})\approx0.809$. Then $x=\frac{77}{0.809}\approx95.2$.

Answer:

95.2 ft