Question

express tan b as a fraction in simplest terms.

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle B$ in right - triangle $BCD$, the side opposite to $\angle B$ is $CD$ and the side adjacent to $\angle B$ is $BC$.

Step2: Use the Pythagorean theorem to find $BC$

By the Pythagorean theorem $BC=\sqrt{BD^{2}-CD^{2}}$. Given $BD = 35$ and $CD=21$, then $BC=\sqrt{35^{2}-21^{2}}=\sqrt{(35 + 21)(35 - 21)}=\sqrt{56\times14}=\sqrt{784}=28$.

Step3: Calculate $\tan B$

$\tan B=\frac{CD}{BC}$. Substituting $CD = 21$ and $BC = 28$, we get $\tan B=\frac{21}{28}=\frac{3}{4}$.

Answer:

$\frac{3}{4}$