Question

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

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 $B$ is $6$, the opposite side to $B$ is $8$, and the hypotenuse is $10$.

Step2: Calculate cosine of angle $B$

$\cos B=\frac{\text{adjacent to }B}{\text{hypotenuse}}=\frac{6}{10}$.

Step3: Calculate tangent of angle $B$

$\tan B=\frac{\text{opposite to }B}{\text{adjacent to }B}=\frac{8}{6}$.

Answer:

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