Question

one side of triangle is double the other and the angles opposite these sides differ by π/3 . show that the angle is right angled triangle​

Answer 1

Using Sine law in the triangle,

sin(θ−60

0

)

a

=

sinθ

2a

⇒

2

1

=

sinθ

sinθ⋅cos60

0

−cosθ⋅sin60

0

⇒1=1−

3

cotθ

⇒cotθ=0

⇒θ=

2

π

Now, one angle is 90

0

, one is 30

0

and the last is 60

0

So, its a right-angled triangle only.