The value of x = 11 and y = 11√3.
Solution:
The triangle is right triangle.
θ = 30° and hypotenuse = 22
The value of sin 30° = [tex]\frac{1}{2}[/tex]
The value of cos 30° = [tex]\frac{\sqrt{3} }{2}[/tex]
Using trigonometric formulas,
[tex]$\sin\theta=\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]$\sin30^\circ=\frac{x}{\text{22}}[/tex]
[tex]$\frac{1}{2} =\frac{x}{\text{22}}[/tex]
Do cross multiplication, we get
22 = 2x
Switch the sides
2x = 22
Divide by 2, we get
x = 11
[tex]$\cos\theta=\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]$\cos30^\circ=\frac{y}{\text{22}}[/tex]
[tex]$\frac{\sqrt{3} }{2} =\frac{y}{\text{22}}[/tex]
Do cross multiplication, we get
[tex]22\sqrt 3 = 2y[/tex]
Switch the sides
[tex]2y=22\sqrt 3[/tex]
Divide by 2, we get
[tex]y= 11\sqrt3[/tex]
Hence the value of x = 11 and y = 11√3.
