Question

trig word problems solve for angle
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.
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Explanation:

Step1: Identify the trig - function

The ladder against the wall forms a right - triangle. The length of the ladder is the hypotenuse ($c = 18$ feet) and the height on the wall is the opposite side ($a=16.9$ feet) with respect to the angle between the ladder and the wall. We use the sine function $\sin\theta=\frac{a}{c}$.

Step2: Calculate the sine of the angle

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 $0.9389$, i.e., $\theta=\sin^{- 1}(0.9389)$. Using a calculator, $\theta\approx70.8^{\circ}$.

Answer:

$70.8^{\circ}$