Question

a fire truck extends a 90 foot ladder toward a building at a 61° angle, to reach a window. how far away is the fire truck from the building? round your answer to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

We know the length of the hypotenuse (ladder length \(c = 90\) feet) and the angle \(\theta=61^{\circ}\), and we need to find the adjacent side \(x\) (distance from fire - truck to building). Use the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(\cos(61^{\circ})=\frac{x}{90}\).

Step2: Solve for \(x\)

Rearrange the formula to \(x = 90\times\cos(61^{\circ})\).
We know that \(\cos(61^{\circ})\approx0.4848\).
Then \(x = 90\times0.4848\).
\(x=43.632\)

Answer:

\(43.63\)