Question

Find the length of AC in the given figure, if the sides are in the ratio $1:\sqrt{3}:2$

• A. $\sqrt{2}$ metres
• B. $\sqrt{5}$ metres
• C. 1 metre
• D. $\sqrt{3}$ metres

Answer 1

The correct option is D

$\sqrt{3}$ metres

$\because$ Sum of all internal angles of a triangle = 180${}^{\circ }$
$\therefore$ Angle A will be 90${}^{\circ }$

In Right-angled triangle ABC, The hypotenuse is given as 2 metres

The other two angles are 30${}^{\circ }$ and 60${}^{\circ }$

The sides are in the ratio $1:\sqrt{3}:2$

Since, hypotenuse is already 2 metres

$\therefore$ The length of AC which is opposite to 60${}^{\circ }$ angle will be $\sqrt{3}$ metres