Question

find tan b
the figure is not drawn to scale.
answer
\frac{33}{55}
\frac{33}{44}
\frac{44}{33}
\frac{44}{55}

Explanation:

Step1: Recall tangent definition

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

Step2: Identify sides for angle B

For angle B, opposite side is 44, adjacent side is 33.

Step3: Calculate $\tan B$

$\tan B = \frac{44}{33}$ (simplify: $\frac{4}{3}$? Wait, no, wait: Wait, the triangle has legs 33 and 44, hypotenuse 55. For angle B, the opposite side is the leg opposite B, which is 44 (since angle B is at the top, so the side opposite is the horizontal leg 44), and adjacent is the vertical leg 33. So $\tan B = \frac{\text{opposite}}{\text{adjacent}} = \frac{44}{33}$? Wait, no, wait: Wait, angle at A is between 44 and 55? Wait, no, the right angle is between 33 and 44. So angle B is at the vertex with side 33 (vertical) and hypotenuse 55. So the sides: for angle B, opposite side is 44 (the horizontal leg), adjacent side is 33 (the vertical leg). So $\tan B = \frac{\text{opposite}}{\text{adjacent}} = \frac{44}{33}$? Wait, but let's check the options. The options include $\frac{44}{33}$? Wait, the third option is $\frac{44}{33}$, fourth is $\frac{4}{3}$? Wait, no, the image shows options: first $\frac{33}{55}$, second $\frac{33}{44}$, third $\frac{44}{33}$, fourth $\frac{4}{3}$? Wait, maybe I misread. Wait, the triangle: right angle between 33 (vertical) and 44 (horizontal), hypotenuse 55. So angle B is at the top, so the sides: opposite to B is 44 (horizontal), adjacent to B is 33 (vertical). So $\tan B = \frac{44}{33}$. So the third option is $\frac{44}{33}$.

Answer:

$\frac{44}{33}$ (or simplified $\frac{4}{3}$, but among the options, the third one is $\frac{44}{33}$)