Question

score:4/10 current time:66.3
find: tan a
right triangle with right angle, vertical side labeled 24 (opposite angle a), horizontal side labeled 18 (adjacent to angle a), hypotenuse labeled 30, angles labeled b (at top) and a (at bottom right)
the figure is not drawn to scale
answer
options: (\frac{18}{24}), (\frac{18}{30}), (\frac{24}{18}), (\frac{24}{30})

Explanation:

Step1: Recall tangent definition

In a right triangle, $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$ to $\theta$.

Step2: Identify sides for $\angle A$

For $\angle A$, opposite side is $24$, adjacent side is $18$.

Step3: Calculate $\tan A$

$\tan A = \frac{\text{opposite to } A}{\text{adjacent to } A} = \frac{24}{18}$

Answer:

$\frac{24}{18}$ (corresponding to the option with $\frac{24}{18}$)