Question

1. a 15 m pole is leaning against a wall. the foot of the pole is 10 m from the wall. find the angle the pole makes with the ground.

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle where the hypotenuse (length of the pole) \(c = 15\) m and the adjacent side (distance of the foot of the pole from the wall) \(a=10\) m. We use the cosine ratio \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Calculate the cosine of the angle

\(\cos\theta=\frac{10}{15}=\frac{2}{3}\)

Step3: Find the angle

\(\theta=\cos^{- 1}(\frac{2}{3})\)
Using a calculator, \(\theta\approx48.19^{\circ}\)

Answer:

The angle the pole makes with the ground is approximately \(48.19^{\circ}\)