Question

use the diagram to answer the questions on the right: 7 three part question: (a) which trig function would you use to find x? a sine b cosine c tangent (b) choose the correct cosine equation: a cos(37) = \frac{x}{11}

Explanation:

Step1: Identify sides relative to angle

In a right - triangle, for the given angle of 37°, the side of length 11 is the adjacent side and x is the hypotenuse.

Step2: Recall trigonometric ratio definitions

The cosine of an angle in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 37^{\circ}$, adjacent = 11, and hypotenuse = x, so $\cos(37^{\circ})=\frac{11}{x}$.

Step3: Answer part (a)

Since we are using the adjacent side and the hypotenuse to find x, we use the cosine function.

Step4: Answer part (b)

The correct cosine equation is $\cos(37^{\circ})=\frac{11}{x}$.

Answer:

(a) B. cosine
(b) None of the given options are correct. The correct equation is $\cos(37^{\circ})=\frac{11}{x}$