Question

In $\Delta$ $ABC$ the sides opposite to angles $A,B,C$ are denoted by $a,b,c$ respectively.

If one side of a triangle is double the other, and the angles on opposite sides differ by ${60}^{\circ },$ then the triangle is

• A. equilateral
• B. obtuse angled
• C. right angled
• D. acute angled

Answer 1

Answer: (C)

right angled

Let $A,B,C$ be the sides and $y,y-60$ be the angles
then side $A=x,C=2x$
and angles $a=y-60,c=y$
$\therefore y+y-60+b=180\Rightarrow b=240-2y$
From sin law
$\frac{2x}{\sin y}=\frac{x}{\sin (y-60)}$
$\Rightarrow 2x\sin (y-60)=x\sin 60\Rightarrow \frac{-\sqrt{3}}{2}\cos =0$
$\Rightarrow \cos y=0\Rightarrow y=90$ or $180$
In triangle $y\ne 180\therefore y=90$
Hence triangle is right angle triangle