Question

If the angles of a triangle ABC are in the ratio 1:2:3, then the corresponding sides are in the ratio:

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

Hint:

Triangles with angles $30^\circ$, $60^\circ$, and $90^\circ$ have side ratios $1:\sqrt{3}:2$

Answer 1

The Correct Option is C

If angle ratio is $1:2:3$, the angles are: \[ x,\ 2x,\ 3x \Rightarrow x + 2x + 3x = 180^\circ \Rightarrow x = 30^\circ \Rightarrow \text{Angles: } 30^\circ,\ 60^\circ,\ 90^\circ \] The side ratios in a triangle with angles $30^\circ$, $60^\circ$, $90^\circ$ are: \[ 1:\sqrt{3}:2 \]