Answer:
The length of x in the simplest radical form with a rational denominator will be:
- [tex]x=\frac{5\sqrt{3}}{2}[/tex]
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
[tex]cos\:60^{\circ }\:=\:\frac{x}{5}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{x}{5}[/tex]
switch sides
[tex]\frac{x}{5}=\frac{\sqrt{3}}{2}[/tex]
Multiply both sides by 5
[tex]\frac{5x}{5}=\frac{5\sqrt{3}}{2}[/tex]
Simplify
[tex]x=\frac{5\sqrt{3}}{2}[/tex]
Therefore, the length of x in the simplest radical form with a rational denominator will be:
- [tex]x=\frac{5\sqrt{3}}{2}[/tex]
