Question

If angles of a triangle are in the ratio of 2 : 3 : 7, then the sides are in the ratio of

• A. $\sqrt{2}:2:(\sqrt{3}+1)$
• B. $\sqrt{2}:\sqrt{2}:(\sqrt{3}+1)$
• C. $\sqrt{2}:(\sqrt{3}+1):2$
• D. $\sqrt{2}:(\sqrt{3}+1):\sqrt{2}$

Answer 1

The correct option is A $\sqrt{2}:2:(\sqrt{3}+1)$

Given that angles of the triangle are in the ratio of $2:3:7$

We know that sum of the angles of the triangle is ${180}^0$

Therefore, $2x+3x+7x=180$

$⟹12x=180$

$⟹x=15$

Therefore, the first angle is $2x=2\ast 15={30}^0$

the second angle is $3x=3\ast 15={45}^0$

and the third angle is $7x=7\ast 15={105}^0$

The sides are in the ratio of $\sin 30:\sin 45:\sin 105$

$=\frac{1}{2}:\frac{1}{\sqrt{2}}:\frac{\sqrt{3}+1}{2\sqrt{2}}$

$=\sqrt{2}:2:\sqrt{3}+1$