Question

question 15 (1 point)
for the given triangle, use one of the reciprocal ratios to determine θ to the nearest degree.

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

Explanation:

Step1: Identify the reciprocal ratio

The cosine of an angle in a right - triangle is given by \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to \(\theta\) is \(12\) and the hypotenuse is \(15\). The reciprocal of cosine is secant, \(\sec\theta=\frac{\text{hypotenuse}}{\text{adjacent}}\). But we can also use \(\cos\theta=\frac{12}{15}=\frac{4}{5}\)

Step2: Calculate the angle

We know that \(\theta=\cos^{- 1}(\frac{12}{15})\). Using a calculator, \(\cos^{-1}(0.8)\approx37^{\circ}\)

Answer:

A. 37