Question

a radio tower has a 7 - foot shadow cast by the sun. if the angle from the tip of the shadow to the top of the tower is 85°, what is the height of the radio tower? round your solution to four decimal places.

Explanation:

Step1: Set up tangent ratio

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let the height of the tower be $h$. The angle $\theta = 85^{\circ}$ and the adjacent - side to the angle (length of the shadow) is $7$ feet. So, $\tan(85^{\circ})=\frac{h}{7}$.

Step2: Solve for $h$

Multiply both sides of the equation by $7$: $h = 7\times\tan(85^{\circ})$.
We know that $\tan(85^{\circ})\approx11.4301$. Then $h = 7\times11.4301=79.9107$.

Answer:

$79.9107$