Question

rico secures a volleyball - net pole to the ground with a rope that is attached to the top of the pole and creates a diagonal distance to the ground. the volleyball - net pole creates a 90° angle to the ground. if the pole is 8 feet in height and rico ties the rope five feet from the base of the pole, what is the angle formed between the top of the pole and the rope? round your answer to the nearest whole degree. (1 point)

○ 34
○ 31
● 12
○ 21

Explanation:

Step1: Identify the right - triangle sides

The height of the pole is the adjacent side ($a = 8$ feet) to the angle we want to find, and the distance from the base of the pole to where the rope is tied is the opposite side ($b = 5$ feet) with respect to the angle $\theta$ between the top of the pole and the rope.

Step2: Use the tangent function

The tangent of an angle $\theta$ in a right - triangle is given by $\tan\theta=\frac{b}{a}$. Substituting $a = 8$ and $b = 5$, we get $\tan\theta=\frac{5}{8}=0.625$.

Step3: Find the angle

To find the angle $\theta$, we take the inverse tangent (arctan) of 0.625. So, $\theta=\arctan(0.625)$. Using a calculator, $\theta\approx32^{\circ}$.

Answer:

32