Question

$ABC$ is a right angled triangle with $\angle BAC={90}^{\circ }$. $AH$ is drawn perpendicular to $BC$. If $AB=60$ cm and $AC=80$ cm, then $BH=$ __________.

• A. $36$ cm
• B. $32$ cm
• C. $24$ cm
• D. $30$ cm

Answer 1

The correct option is A $36$ cm

Consider $△$ $ABC$ and $△$ $BAH$

$\cos \left(\angle ABC\right)=\frac{AB}{BC}$ ($\because △ABC$ is a right angled triangle and from definition of cos)

$\cos \left(\angle ABH\right)=\frac{BH}{AB}$ ($\because △ABH$ is a right angled triangle and from definition of cos)

$\angle ABC=\angle ABH$

$\Rightarrow \frac{AB}{BC}=\frac{BH}{AB}$

$\Rightarrow BH=\frac{AB\times AB}{BC}=\frac{60\times 60}{100}=36$ cm

Option (A) is correct.