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

Find the length of side x simplest radical form with a rational denominator-example-1
User Ma Guowei
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1 Answer

11 votes

Answer:

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)
User Foibs
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