Question

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

Explanation:

Step1: Recall tangent definition

For an acute angle in a right triangle, $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$

Step2: Identify sides for $67^\circ$

Opposite side = 12, Adjacent side = 5

Step3: Calculate $\tan 67^\circ$

$\tan 67^\circ = \frac{12}{5}$

Answer:

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