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Question

The angles of a triangle are in the ratio 3:5:10. Then, the ratio of the smallest side to the greatest side is


A

1:sin10°

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B

1:2sin10°

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C

1:cos10°

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D

1:2cos10°

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Solution

The correct option is D

1:2cos10°


Explanation for the correct option:

Finding the the ratio of the smallest side to the greatest side:

In ABC

A+B+C=180°

Let the angle ratio be 3x,5x,10x

3x+5x+10x=180°18x=180°x=10°

Using sine rule

asinA=bsinB=csinC=kac=ksinAksinCac=sin3xsin10x[A=3x;C=10x]ac=sin3×10°sin2×10°[x=10°]ac=sin30°sin100°=12sin(90°+10°)[sin30°=12]ac=12cos10°[sin(90°+θ)=cosθ]a:c=1:2cos10

Hence, option (D) is the correct answer.


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