Question

according to this diagram, what is tan 67°?
a. $\frac{12}{13}$
b. $\frac{12}{5}$
c. $\frac{5}{13}$
d. $\frac{5}{12}$
e. $\frac{13}{5}$
f. $\frac{13}{12}$

Explanation:

Step1: Recall tangent - ratio formula

The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify opposite and adjacent sides for 67°

For the 67° angle in the given right - triangle, the side opposite to the 67° angle has length 12 and the side adjacent to the 67° angle has length 5.

Step3: Calculate $\tan67^{\circ}$

$\tan67^{\circ}=\frac{12}{5}$.

Answer:

B. $\frac{12}{5}$