Question

triangle abc is shown. what is cos(∠bac)? choose 1 answer: a $\frac{2sqrt{5}}{5}$ b $\frac{sqrt{5}}{5}$ c 2 d $sqrt{5}$

Explanation:

Step1: Recall cosine - ratio formula

$\cos(\angle BAC)=\frac{adjacent}{hypotenuse}$

Step2: Identify adjacent and hypotenuse

Adjacent to $\angle BAC$ is $AC = 4$, hypotenuse $AB=4\sqrt{5}$

Step3: Calculate cosine value

$\cos(\angle BAC)=\frac{4}{4\sqrt{5}}=\frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5}$

Answer:

B. $\frac{\sqrt{5}}{5}$