Question

triangle abc is shown. what is tan(∠bac)? choose 1 answer: a $\frac{5sqrt{41}}{41}$ b $\frac{4sqrt{41}}{41}$ c $\frac{5}{4}$ d $\frac{4}{5}$

Explanation:

Step1: Recall tangent - ratio formula

The formula for the tangent of an angle in a right - triangle is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle BAC$, the opposite side to $\angle BAC$ is $BC$ and the adjacent side is $AC$.

Step2: Identify side lengths

From the right - triangle $ABC$, we have $BC = 4$ and $AC=5$.

Step3: Calculate the tangent value

$\tan(\angle BAC)=\frac{BC}{AC}=\frac{4}{5}$.

Answer:

D. $\frac{4}{5}$