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Question

In a right-angled triangle, one acute angle is double the other, then the hypotenuse is


A

Equal to the smallest side

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B

Double the smallest side

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C

Triple the smallest side

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D

None of these

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Solution

The correct option is B

Double the smallest side


Step-1: Draw ABC

Let BAC=x

then ACB=2x

ABC=90°

Step-2: Find the smallest side of ABC

In ABC,

ABC+BAC+ACB=180°.......(1) ( Angle Sum Property )

On putting values in (1)

90°+x+2x=180°

x=BAC=30°

ACB=2×30°=60°

The side opposite the smallest angle is the smallest.

Hence, BC is the smallest side of the triangle.

Step-3: Find the relation between the hypotenuse and the smallest side.

In ABC,

cos2x=BCAC

cos60°=BCAC

12=BCACcos60°=12

AC=2·BC

So, Hypotenuse is double the smallest side.

Hence, option (B) is the correct answer.


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