Question

express tan b as a fraction in simplest terms.
answer attempt 1 out of 5
tan b =

Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle B\), the side opposite to \(\angle B\) is \(CD = 10\) and the side adjacent to \(\angle B\) is \(BC=24\).

Step2: Calculate \(\tan B\)

Using the formula \(\tan B=\frac{CD}{BC}\), substitute \(CD = 10\) and \(BC = 24\). So, \(\tan B=\frac{10}{24}\).

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor. The GCD of \(10\) and \(24\) is \(2\). \(\frac{10\div2}{24\div2}=\frac{5}{12}\).

Answer:

\(\frac{5}{12}\)