Question

triangle abc is shown. what is cos(∠bac)? choose 1 answer: a 7/√74 b 5√74/74 c 7√74/74 d 5/7

Explanation:

Step1: Recall cosine - ratio formula

In a right - triangle, $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle BAC$, the adjacent side to $\angle BAC$ is $AC = 7$ and the hypotenuse is $AB=\sqrt{74}$.

Step2: Calculate $\cos(\angle BAC)$

Using the formula $\cos(\angle BAC)=\frac{AC}{AB}$, we substitute $AC = 7$ and $AB=\sqrt{74}$. So, $\cos(\angle BAC)=\frac{7}{\sqrt{74}}$. Rationalizing the denominator by multiplying the numerator and denominator by $\sqrt{74}$, we get $\cos(\angle BAC)=\frac{7\sqrt{74}}{74}$.

Answer:

C. $\frac{7\sqrt{74}}{74}$