Question

a 81.4 - foot rope from the top of a circus tent pole is anchored to the ground 50.9 feet from the bottom of the pole. what angle does the rope make with the pole? (assume the pole is perpendicular to the ground.) round to at least 1 decimal place.

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the length of the rope is the hypotenuse $c = 81.4$ feet and the distance from the bottom of the pole to the anchor point is the side opposite the angle $\theta$ we want to find, $a = 50.9$ feet. We use the sine function, $\sin\theta=\frac{a}{c}$.

Step2: Calculate the sine of the angle

$\sin\theta=\frac{50.9}{81.4}$
$\sin\theta\approx0.6253$

Step3: Find the angle

$\theta=\sin^{- 1}(0.6253)$
$\theta\approx38.7^{\circ}$

Answer:

$38.7^{\circ}$