Question

Find the value of $\tan B$ in the right angled triangle shown above, given that the measure of $\angle C$ is ${90}^{\circ }$, $AB=5$ units and $CB=2$ units.

• A. $\frac{\sqrt{21}}{2}$
• B. $\frac{3}{2}$
• C. $\frac{\sqrt{21}}{5}$
• D. $\frac{3}{5}$
• E. $\frac{2}{5}$

Answer 1

The correct option is A $\frac{\sqrt{21}}{2}$

In a right-angled triangle with angle $C=$ ${90}^{\circ }$

Using Pythagorean theorem

$(AB{)}^2=(BC{)}^2+(AC{)}^2$

$(AC{)}^2=(AB{)}^2-(BC{)}^2$

$AC=\sqrt{(AB{)}^2-(BC{)}^2}$

Put the value from the figure, we get

$AC=\sqrt{5^2-2^2}$

$AC=\sqrt{25-4}$

$AC=\sqrt{21}$

$\tan B=$ $\frac{Perpendicular}{Base}=\frac{AC}{BC}=\frac{\sqrt{21}}{2}$