Question

Given ABC, which of the following ratios is equivalent to cos B?

Answer 1

Given:

The measure of side AC is 15.

The measure of side BC is 36.

The objective is to fnd the correct option of cos B.

The measure of length AC can be calculated as using Pythagorean theorem.

`\begin{gathered} AC^2=AB^2+BC^2 \\ AC^2=15^2+36^2 \\ AC^2=225+1296 \\ AC^2=1521 \\ AC=\sqrt[]{1521} \\ AC=39 \end{gathered}`

Now, by considering angle B, the side AC is opposite side, BC is adjacent side and AC is hypotenuse side.

Then, the ratio of cos B can be calculated as,

`\begin{gathered} \cos \text{B=}\frac{\text{adjacent}}{hypotenuse} \\ =(36)/(39) \\ =(12)/(13) \end{gathered}`

Hence, option (C) is the correct answer.