Question

1. a fireman leaned a 36 - foot ladder against a building. if he placed the ladder 7 feet from the base of the building, what angle is formed between the ladder and the ground?

Explanation:

Step1: Identify the trigonometric ratio

We know the adjacent side (\(a = 7\)) and the hypotenuse (\(c=36\)) of a right - triangle. We use the cosine ratio \(\cos\theta=\frac{a}{c}\).
So, \(\cos\theta=\frac{7}{36}\).

Step2: Find the angle

To find \(\theta\), we use the inverse cosine function \(\theta=\cos^{- 1}(\frac{7}{36})\).
Using a calculator, \(\theta\approx78.7^{\circ}\)

Answer:

The angle formed between the ladder and the ground is approximately \(78.7^{\circ}\)