Question

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

Options

• Isosceles

• Right-angled

• Obtuse angled

• Acute angled

Answer 1

If one side of a triangle is double the other and the angles opposite to these sides differ by 60°, then the triangle is Right-angled.

Explanation:

`sinA/a = sinB/b = sinC/c`

According to the given condition,

In ΔABC, a = 2b and

A - B = 60° ⇒ A = 60° + B

⇒ `(sin(60^circ + B))/(2b) = sinB/b`

⇒ `sinB/(sin(B + 60^circ)) = 1/2`

⇒ 2 sin B = sin B cos 60° + cos B sin 60°

⇒ `3/2 sinB = sqrt3/2 cosB`

∴ `tanB = 1/sqrt3 ⇒ B = 30^circ`

∴ A = 30° + 60° = 90°

∴ ΔABC is right angled .