Question

a 32 - foot ladder is leaning against a building and forms a 29.37° angle with the ground. how far away from the building is the base of the ladder? round your answer to the nearest hundredth.
15.69 feet
18.01 feet
27.89 feet
36.72 feet

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the ladder is the hypotenuse ($c = 32$ feet) and we want to find the adjacent side ($x$) to the given angle $\theta=29.37^{\circ}$. We use the cosine function: $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos\theta=\frac{x}{c}$

Step2: Solve for $x$

Substitute $\theta = 29.37^{\circ}$ and $c = 32$ into the formula.
$x = c\times\cos\theta$
$x=32\times\cos(29.37^{\circ})$
We know that $\cos(29.37^{\circ})\approx0.87156$.
$x = 32\times0.87156=27.89$ feet

Answer:

C. 27.89 feet