Question

a wire makes a 20° angle with the ground and is attached to the top of a 50 ft antenna. how long is the wire? round to the near

Explanation:

Step1: Identify trig - relation

We have a right - triangle where the height of the antenna is the opposite side to the given angle and the wire is the hypotenuse. We use the sine function, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 20^{\circ}$ and the opposite side $y = 50$ ft, and the hypotenuse is $x$ (the length of the wire). So, $\sin(20^{\circ})=\frac{50}{x}$.

Step2: Solve for $x$

We can re - arrange the equation $\sin(20^{\circ})=\frac{50}{x}$ to get $x=\frac{50}{\sin(20^{\circ})}$. Since $\sin(20^{\circ})\approx0.3420$, then $x=\frac{50}{0.3420}\approx146.2$.

Answer:

$146$ ft