Question

emma leans a 28 - foot ladder against a wall. if the ladder reaches 24.5 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 ($c = 28$) and the height on the wall is the opposite side ($a=24.5$) 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, $\sin\theta=\frac{24.5}{28}$.

Step2: Calculate the value of the ratio

$\frac{24.5}{28}=0.875$.

Step3: Find the angle using the inverse sine function

If $\sin\theta = 0.875$, then $\theta=\sin^{- 1}(0.875)$.
Using a calculator, $\sin^{-1}(0.875)\approx61.0^{\circ}$.

Answer:

$61.0^{\circ}$