Question

what is tan b? a. \\(\frac{2}{3}\\) b. \\(\frac{3}{2}\\) c. \\(\frac{\sqrt{13}}{2}\\) d. \\(\frac{\sqrt{13}}{3}\\) (triangle with right angle at a, ab=2, ac=3, bc=\\(\sqrt{13}\\))

Explanation:

Step1: Recall tangent definition

For right triangle $\triangle ABC$ (right-angled at $A$), $\tan B = \frac{\text{opposite side to } B}{\text{adjacent side to } B}$

Step2: Identify relevant sides

Opposite side to $B$ is $AC=3$, adjacent side is $AB=2$.

Step3: Calculate $\tan B$

$\tan B = \frac{AC}{AB} = \frac{3}{2}$

Answer:

B. $\frac{3}{2}$