Question

express tan b as a fraction in simplest terms.

Explanation:

Step1: Find the length of BC

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 35\), \(b = 21\), and \(a=BC\).

$$BC=\sqrt{35^{2}-21^{2}}=\sqrt{(35 + 21)(35 - 21)}=\sqrt{56\times14}=\sqrt{784}=28$$

Step2: Calculate \(\tan B\)

The definition of \(\tan\) in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle B\), the opposite side to \(\angle B\) is \(CD = 21\), and the adjacent side to \(\angle B\) is \(BC = 28\).
\(\tan B=\frac{CD}{BC}=\frac{21}{28}\)
Simplify the fraction \(\frac{21}{28}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 7.
\(\frac{21\div7}{28\div7}=\frac{3}{4}\)

Answer:

\(\frac{3}{4}\)