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If one side of a triangle is double the ...

If one side of a triangle is double the other, and the angles on opposite sides differ by `60^(@)`, then the triangle is

A

equilateral

B

obtus angled

C

right angled

D

acute angled

Text Solution

Verified by Experts

The correct Answer is:
C
`a = 2b and A - B = 60^(@)`
We know that `tan.(A -B)/(2) = (a -b)/(a + b) cot.(C)/(2)`
or `tan 30^(@) = (1)/(3) cot.(C)/(2)`
or `tan.(C)/(2) = (1)/(sqrt3) " or " C = 60^(@)`
Hence, `A + B = 20^(@) " or " 2A = 180^(@)`
`rArr A = 90^(@), B = 30^(@), C = 60^(@)`
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Knowledge Check

  • If one side of a triangle is double the other and the angles opposite to these sides differ by 60^@ , then the triangle is

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    B
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