Question

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

Answer 1

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

• 
  `x=(5√(3))/(2)`

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 )\:=\:(x)/(5)`

`(√(3))/(2)=(x)/(5)`

switch sides

`(x)/(5)=(√(3))/(2)`

Multiply both sides by 5

`(5x)/(5)=(5√(3))/(2)`

Simplify

`x=(5√(3))/(2)`

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

• 
  `x=(5√(3))/(2)`