Question

trig word problems solve for angle score: 2/3 penalty: none question juan leans a 18 - foot ladder against a wall. if the ladder reaches 16.9 feet up the wall, what angle does it form with the wall? round your answer to the nearest tenth of a degree. answer attempt 1 out of 2

Explanation:

Step1: Identify right - triangle elements

We have a right - triangle where the hypotenuse (length of the ladder) $c = 18$ feet and the opposite side to the angle we want to find (height on the wall) $a=16.9$ feet.

Step2: Use sine function

The sine of an angle $\theta$ in a right - triangle is given by $\sin\theta=\frac{a}{c}$. Substituting $a = 16.9$ and $c = 18$, we get $\sin\theta=\frac{16.9}{18}\approx0.9389$.

Step3: Find the angle

To find $\theta$, we take the inverse - sine of $0.9389$, i.e., $\theta=\sin^{- 1}(0.9389)$. Using a calculator, $\theta\approx70.8^{\circ}$.

Answer:

$70.8$