Question

Find the length of side x in simplest radical form with a rational denominator.

Answer 1

Answer:

$x = \frac{\sqrt{6}}{2}$

Step-by-step explanation:

Reference angle = 45°

Opposite side = x

Hypotenuse = √3

Use the following trigonometric ratios formula to find x:

$sin(\theta) = \frac{opp}{hyp}$

Plug in the values

$sin(45) = \frac{x}{\sqrt{3}}$

Multiply both sides by √3

$\sqrt{3}*sin(45) = x$

$\sqrt{3}*\frac{\sqrt{2}}{2} = x$

$\frac{\sqrt{3*2}}{2} = x$

$\frac{\sqrt{6}}{2} = x$