Question

express tan b as a fraction in simplest terms.
answer attempt 1 out of 2
tan b =

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle B$, the opposite side to $\angle B$ is $CD = 21$ and the adjacent side is $BC$. We first need to find $BC$ using the Pythagorean theorem.
Let $BC = x$. In right - triangle $BCD$ with hypotenuse $BD = 35$ and one side $CD = 21$, by the Pythagorean theorem $x^{2}+21^{2}=35^{2}$. So $x^{2}=35^{2}-21^{2}=(35 + 21)(35 - 21)$ (using $a^{2}-b^{2}=(a + b)(a - b)$). Then $x^{2}=(56)(14)=784$, and $x = 28$.

Step2: Calculate $\tan B$

Now that we know the opposite side to $\angle B$ is $21$ and the adjacent side is $28$, $\tan B=\frac{21}{28}$. Simplifying the fraction $\frac{21}{28}$ by dividing both the numerator and denominator by 7, we get $\tan B=\frac{3}{4}$.

Answer:

$\frac{3}{4}$