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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 $$BH =$$ __________.
724266_520ffab0fb4e403db36ff5425fa7c79b.png


A
36 cm
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B
32 cm
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C
24 cm
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D
30 cm
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Solution

The correct option is A $$36$$ cm
Consider $$\triangle $$ $$ABC$$ 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)

$$\angle ABC=\angle ABH$$

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

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

Option (A) is correct.

Mathematics

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