rico secures a volleyball-net pole to the ground with a rope that is attached to the top of the pole and…

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 $90^{\\circ}$ angle to the ground. if the pole is eight 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)

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 $90^{\\circ}$ angle to the ground. if the pole is eight 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)

Answer

Explanation:

Step1: Identify the right triangle components

The pole (height $h = 8$ ft) and the ground distance ($d = 5$ ft) form the legs of a right triangle.

Step2: Determine the target angle

The angle $\theta$ is between the pole and the rope at the top.

Step3: Select the trigonometric ratio

In this triangle, the side opposite $\theta$ is the ground distance ($5$ ft) and the adjacent side is the pole height ($8$ ft). $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{8}$$

Step4: Calculate the angle using arctangent

Solve for $\theta$ by taking the inverse tangent of the ratio. $$\theta = \arctan\left(\frac{5}{8}\right)$$

Step5: Evaluate and round the result

Calculate the numerical value and round to the nearest whole degree. $$\theta \approx 32.005^{\circ}$$

Answer:

32 degrees