Question

question 15 (1 point)
for the given triangle, use one of the reciprocal ratios to determine \\( \theta \\) to the nearest

degree.

a) 37
b) 39
c) 38
d) 40

Explanation:

Step1: Identify the reciprocal ratio

The reciprocal ratio of cosine is secant. $\sec\theta=\frac{\text{hypotenuse}}{\text{adjacent}}$. Here, hypotenuse = 15 and adjacent = 12. So, $\sec\theta=\frac{15}{12}=\frac{5}{4}$.

Step2: Find the angle

Since $\sec\theta=\frac{5}{4}$, then $\theta=\sec^{- 1}(\frac{5}{4})$. Also, $\sec\theta=\frac{1}{\cos\theta}$, so $\cos\theta=\frac{4}{5}$. Using the inverse - cosine function, $\theta=\cos^{-1}(\frac{4}{5})$.
Using a calculator, $\cos^{-1}(\frac{4}{5})\approx37^{\circ}$.

Answer:

a) 37