Question

In a $△ABC$ right angled at $C$, if $\tan A=\frac{3}{4}$ then what is the value of $\cot B=\frac{m}{4}$.Find $m$

Answer 1

Solution:-

In a triangle, sum of all the angle will be $180°$.

$\therefore \angle A+\angle B+\angle C=180°$

$\Rightarrow \angle A+\angle B+90°=180°\{\because \angle C=90°\left(Given\right)\}$

$\Rightarrow \angle A+\angle B=180°-90°$

$\Rightarrow \angle B=(90°-\angle A)$

$\therefore \cot B=\cot (90°-A)$

$\Rightarrow \cot B=\tan A\{\because \cot (90°-\theta )=\tan \theta \}$

$\therefore \cot B=\frac{3}{4}⟶\left(i\right)\{\because \tan A=\frac{3}{4}\left(Given\right)\}$

$\cot B=\frac{m}{4}⟶\left(ii\right)$

From ${eq}^n\left(i\right)\&\left(ii\right)$, we have

$\frac{m}{4}=\frac{3}{4}$

$\Rightarrow m=3$

Hence, $m=3$.