express $\tan b$ as a fraction in simplest terms.\nanswer attempt 1 out of 2\n$\tan b =$

Explanation:

Step1: Find side BC via Pythagoras

For right triangle BCD: $$BC = \sqrt{BD^2 - CD^2} = \sqrt{35^2 - 21^2}$$ $$=\sqrt{1225 - 441} = \sqrt{784} = 28$$

Step2: Define tan B for angle B

$\tan B = \frac{\text{opposite to } B}{\text{adjacent to } B} = \frac{CD}{BC}$

Step3: Simplify the fraction

$$\tan B = \frac{21}{28} = \frac{3}{4}$$

Answer:

$\frac{3}{4}$