Question

lauren leans a 30-foot ladder against a wall. if the ladder reaches 27.2 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

We have a right - triangle where the ladder is the hypotenuse ($c = 30$) and the height on the wall is the opposite side ($a=27.2$) with respect to the angle $\theta$ (the angle between the ladder and the ground). We use the sine ratio: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
So, $\sin\theta=\frac{27.2}{30}$.

Step2: Solve for $\theta$

Take the inverse sine (arcsin) of both sides: $\theta=\sin^{- 1}(\frac{27.2}{30})$.
Calculate $\frac{27.2}{30}\approx0.9067$.
Then $\theta=\sin^{-1}(0.9067)$.
Using a calculator, $\theta\approx64.0^{\circ}$.

Answer:

$64.0^{\circ}$