Question

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

Answer 1

Answer:

The length of x in the simplest radical form with a rational denominator will be:      

•       $x=\frac{5\sqrt{3}}{2}$

Step-by-step explanation:

Given

hypotenuse = 5

angle Ф = 60°

To determine

x = ?

Using the trigonometric ratio

cos Ф = adjacent / hypotenuse

here

Ф = 60°

adjacent of 60° = x

hypotenuse = 5

so substituting Ф = 60°, adjacent = x and hypotenuse = 5 in the equation

cos Ф = adjacent / hypotenuse

so

$cos\:60^{\circ }\:=\:\frac{x}{5}$

       $\frac{\sqrt{3}}{2}=\frac{x}{5}$

switch sides

         $\frac{x}{5}=\frac{\sqrt{3}}{2}$

Multiply both sides by 5

         $\frac{5x}{5}=\frac{5\sqrt{3}}{2}$

Simplify

         $x=\frac{5\sqrt{3}}{2}$

Therefore, the length of x in the simplest radical form with a rational denominator will be:      

•       $x=\frac{5\sqrt{3}}{2}$