To begin with, we will have to sketch the image of the question
To find the value of tan B
we will make use of the trigonometric identity
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]From the diagram given
[tex]\tan B=\frac{\text{opposite}}{\text{adjacent}}=\frac{b}{96}[/tex]Since the value of b is unknown, we will have to get the value of b
To do so, we will use the Pythagorean theorem
[tex]\begin{gathered} \text{hypoteuse}^2=\text{opposite}^2+\text{adjacent}^2 \\ b^2=100^2-96^2 \\ b=\sqrt[]{784} \\ b=28 \end{gathered}[/tex]Since we now know the value of b, we will then substitute this value into the tan B function
so that we will have
[tex]\tan \text{ B=}\frac{opposite}{adjecent}=\frac{b}{a}=\frac{28}{96}=\frac{7}{24}[/tex]Therefore
[tex]\tan \text{ B=}\frac{7}{24}[/tex]
