Question

1. a 35 - foot guide wire is attached to a power pole and anchored to the ground 28 ft away. what is the measure of ∠b. show your work #1

Explanation:

Step1: Identify the trigonometric ratio

We know the adjacent side ($28$ ft) and the hypotenuse ($35$ ft) of the right - triangle. The cosine ratio is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Let $\theta = \angle B$. Then $\cos B=\frac{28}{35}$.

Step2: Simplify the ratio

Simplify $\frac{28}{35}=\frac{4}{5} = 0.8$.

Step3: Find the angle using the inverse cosine function

We know that if $\cos B = 0.8$, then $B=\cos^{-1}(0.8)$. Using a calculator, $\cos^{-1}(0.8)\approx37^{\circ}$.

Answer:

$37^{\circ}$