Question

question 24 (1 point) saved
for the given triangle, use one of the reciprocal ratios to determine θ to the nearest degree.
9
15
12
a) 38
b) 37
c) 40
d) 39

Explanation:

Step1: Identify the reciprocal ratio

We know that \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), and the reciprocal of \(\cos\theta\) is \(\sec\theta=\frac{\text{hypotenuse}}{\text{adjacent}}\). Here, adjacent side \(= 12\), hypotenuse \(= 15\). So \(\sec\theta=\frac{15}{12}=\frac{5}{4}\)

Step2: Find \(\theta\)

Since \(\sec\theta=\frac{5}{4}\), then \(\cos\theta=\frac{4}{5}\) (because \(\cos\theta=\frac{1}{\sec\theta}\)). Using the inverse - cosine function \(\theta=\cos^{- 1}(\frac{4}{5})\)

We know that \(\cos^{-1}(x)\) can be calculated. \(\cos^{-1}(\frac{4}{5})\approx37^{\circ}\)

Answer:

B. 37