Question

question 19 (1 point) for the given triangle, use one of the reciprocal ratios to determine θ to the nearest degree. a) 39 b) 38 c) 37 d) 40

Explanation:

Step1: Identify the reciprocal ratio

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

Step2: Use the inverse cosine function

\(\theta = \cos^{-1}(\frac{4}{5})\).
Using a calculator, \(\cos^{-1}(0.8)\approx37^{\circ}\)

Answer:

C. 37