Question

question 11 (5 points)
determine the measure of ∠θ using a trigonometric ratio.
a) 1.00°
b) 45.10°
c) 17.38°
d) 12.54°

Explanation:

Step1: Identify the trig - ratio

In right - triangle $ABC$ with right - angle at $A$, the adjacent side to $\angle\theta$ is $AC = 12$ and the hypotenuse is $BC = 17$. We use the cosine ratio, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos\theta=\frac{12}{17}$.

Step2: Find the angle

To find $\theta$, we take the inverse cosine of $\frac{12}{17}$. That is, $\theta=\cos^{- 1}(\frac{12}{17})$. Using a calculator, $\theta=\cos^{-1}(\frac{12}{17})\approx45.10^{\circ}$.

Answer:

B. $45.10^{\circ}$