Question

tallulah leans a 22 - foot ladder against a wall. if the ladder reaches 19.9 feet up the wall, what angle does it form with the ground? round your answer to the nearest tenth of a degree.

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle where the ladder is the hypotenuse ($c = 22$) and the height on the wall is the opposite side ($a=19.9$) 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, $\sin\theta=\frac{19.9}{22}$.

Step2: Solve for $\theta$

Take the inverse sine (arcsin) of both sides: $\theta=\sin^{- 1}(\frac{19.9}{22})$.

Calculate $\frac{19.9}{22}=0.904545\cdots$.

Then $\theta=\sin^{-1}(0.904545\cdots)$.

Using a calculator, $\theta\approx64.8^{\circ}$.

Answer:

$64.8^{\circ}$