Question

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 the trig - ratio

We have a right - triangle where the hypotenuse is the length of the ladder ($c = 18$ feet) and the opposite side to the angle we want to find is the height the ladder reaches up the wall ($a=16.9$ feet). We use the sine function, $\sin\theta=\frac{a}{c}$.

Step2: Calculate the sine value

Substitute $a = 16.9$ and $c = 18$ into the sine formula: $\sin\theta=\frac{16.9}{18}\approx0.9389$.

Step3: Find the angle

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

Answer:

$70.8^{\circ}$