Question

according to this diagram, what is $\tan 74^circ$?
a. $\frac{7}{25}$
b. $\frac{7}{24}$
c. $\frac{25}{24}$
d. $\frac{25}{7}$
e. $\frac{24}{7}$
f. $\frac{24}{25}$

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 $74^\circ$

Opposite side to $74^\circ$ is 24, adjacent side is 7.

Step3: Calculate $\tan 74^\circ$

$\tan 74^\circ = \frac{24}{7}$

Answer:

E. $\frac{24}{7}$