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Question

If D is the mid-point of BC of a right angled triangle ABC, (BAC=90o) such that triangle ADC is an equilateral Δ then a2:b2:c2 is?

A
1:3:4
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B
3:1:4
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C
4:3:1
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D
4:1:3
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Solution

The correct option is D 4:1:3
Given that A=π2
Since, ADC is an equilateral triangle.
Therefore, C=DAC=π3
B=πAC=π6
Now from sine rule: a2:b2:c2=sin2A:sin2B:sin2C=sin2π2:sin2π6:sin2π3
a2:b2:c2=1:14:34=4:1:3

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