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

Solution

## The correct option is A $$36$$ cmConsider $$\triangle$$ $$ABC$$ and $$\triangle$$ $$BAH$$$$\cos(\angle ABC)=\dfrac{AB}{BC}$$      ($$\because \triangle ABC$$ is a right angled triangle and from definition of cos) $$\cos(\angle ABH)=\dfrac{BH}{AB}$$     ($$\because \triangle ABH$$ is a right angled triangle and from definition of cos)$$\angle ABC=\angle ABH$$$$\Rightarrow \dfrac{AB}{BC}=\dfrac{BH}{AB}$$$$\Rightarrow BH=\dfrac{AB\times AB}{BC}=\dfrac{60\times 60}{100}=36$$ cmOption (A) is correct.Mathematics

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