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), the angle with the ground is \(\theta=29.37^\circ\), and we need to find the adjacent side (\(a\)) to the angle (distance from the building). We use the cosine function: \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(a = c\times\cos(\theta)\).

Step2: Substitute the values

Substitute \(c = 32\) and \(\theta = 29.37^\circ\) into the formula: \(a=32\times\cos(29.37^\circ)\).
First, calculate \(\cos(29.37^\circ)\approx0.8716\). Then \(a = 32\times0.8716 = 27.8912\approx27.89\) (rounded to the nearest hundredth).

Answer:

27.89 feet (corresponding to the option "27.89 feet")