Question

which equation can be used to find b in the triangle? cos b = 10/6 cos b = 10/8 tan b = 8/6 tan b = 8/10

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$ and $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$ with respect to an angle $\theta$. For angle $B$, the adjacent side to angle $B$ is $AB = 6$, the opposite side to angle $B$ is $AC = 8$, and the hypotenuse is $BC = 10$.

Step2: Calculate cosine and tangent of angle $B$

$\cos B=\frac{AB}{BC}=\frac{6}{10}$, and $\tan B=\frac{AC}{AB}=\frac{8}{6}$.

Answer:

$\tan B=\frac{8}{6}$