Question

nathan leans a 20 - foot ladder against a wall. if the ladder reaches 18.9 feet up the wall, what angle does it form with the ground? round your answer to the nearest tenth of a degree. answer attempt 1 out of 2

Explanation:

Step1: Identify the trigonometric ratio

The ladder forms a right - triangle with the wall and the ground. The length of the ladder is the hypotenuse ($c = 20$ feet) and the height on the wall is the opposite side to the angle we want to find ($a=18.9$ feet). We use the sine ratio $\sin\theta=\frac{a}{c}$.

Step2: Calculate the sine of the angle

Substitute $a = 18.9$ and $c = 20$ into the sine formula: $\sin\theta=\frac{18.9}{20}=0.945$.

Step3: Find the angle

To find the angle $\theta$, we take the inverse - sine of 0.945, i.e., $\theta=\sin^{- 1}(0.945)$. Using a calculator, $\theta\approx70.9^{\circ}$.

Answer:

$70.9^{\circ}$