# What is value of x?

Mar 28, 2017

$x = 4$

#### Explanation:

Given that $\Delta R S T$ is a right triangle
$\sin 60 = \frac{R S}{R T}$
$\implies R T = \frac{R S}{\sin} 60 = \frac{2 \sqrt{3}}{\frac{\sqrt{3}}{2}}$
$\implies R T = 2 \sqrt{3} \cdot \left(\frac{2}{\sqrt{3}}\right) = 4$

$\angle R Q T = 180 - 90 - 45 = {45}^{\circ}$
$\implies \angle R Q T = \angle R T Q = {45}^{\circ}$
$\implies \Delta R Q T$ is an isosceles right triangle,
$\implies R Q = R T$
$\implies x = R T = 4$