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

Question

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

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

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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^(@)`

5 views Answered 2023-02-05 15:29