Question

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

Answer 1

Answer:

The value of x = 1

Step-by-step explanation:

Given

• hypotenuse = √2

• angle Ф = 45°

To determine

x = ?

Using the trigonometric ratio

cos Ф = adjacent / hypotenuse

here

Ф = 45°

adjacent of 45° = x

hypotenuse = √2

so substituting Ф = 45°  adjacent = x and hypotenuse = √2  in the equation

cos Ф = adjacent / hypotenuse

$\cos \left(45^{\circ \:}\right)=\frac{x}{\sqrt{2}}$

switch sides

$\frac{x}{\sqrt{2}}=\cos \left(45^{\circ \:}\right)$

Multiply both sides by 2

$\frac{2x}{\sqrt{2}}=2\cos \left(45^{\circ \:}\right)$

$\sqrt{2}x=\sqrt{2}$             ∵  $\cos \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}$

Divide both sides by √2

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

$x=1$

Therefore, the value of x = 1