Question

multiple choice 1 point
a flagpole stands in the middle of a flat, level field. 50 feet away from its base, a surveyor measures the angle to the top of the flagpole as 48 degrees. how tall is the flagpole? round to the nearest hundredth of a foot.
37.16 feet
45.02 feet
33.46 feet
55.53 feet

Explanation:

Step1: Set up tangent - ratio equation

We have a right - triangle where the adjacent side to the angle of elevation is $x = 50$ feet and the opposite side is the height of the flagpole $h$. The tangent of an angle $\theta$ in a right - triangle is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 48^{\circ}$ and the adjacent side $a = 50$ feet. So, $\tan(48^{\circ})=\frac{h}{50}$.

Step2: Solve for $h$

Multiply both sides of the equation $\tan(48^{\circ})=\frac{h}{50}$ by 50. We know that $\tan(48^{\circ})\approx1.1106$. Then $h = 50\times\tan(48^{\circ})$. Substituting the value of $\tan(48^{\circ})$, we get $h=50\times1.1106 = 55.53$ feet.

Answer:

D. 55.53 feet