Question

What is the value of x in simplest radical form?

Answer 1

Answer:

D. $x = \frac{5*\sqrt{2}}{2}$

Step-by-step explanation:

Reference angle = 45°

Length of Opposite side = x

Hypotenuse length = 5

Applying trigonometric ratio, we have:

$sin(45) = \frac{x}{5}$

Multiply both sides by 5

$5*sin(45) = \frac{x}{5}*5$

$5*sin(45) = x$

$5*\frac{1}{\sqrt{2}} = x$ (sin 45 = 1/√2)

$\frac{5}{\sqrt{2}} = x$

Rationalize

$\frac{5*\sqrt{2}}{\sqrt{2}*\sqrt{2}} = x$

$x = \frac{5*\sqrt{2}}{2}$