Answer :
Given:
In the given triangle,
With respect to 30°, the perpendicular = 9, the base = x and the hypotenuse = y
To find the value of x and y.
Formula
By Trigonometric ratio we get,
[tex]sin\theta = \frac{opposite}{Hypotenuse}[/tex] and
[tex]tan\theta =[/tex] [tex]\frac{opposite}{adjacent}[/tex]
Now,
Putting, perpendicular = 9 and [tex]\theta=30^\circ[/tex] we get,
[tex]sin30^\circ = \frac{9}{y}[/tex]
or, [tex]\frac{1}{2} = \frac{9}{y}[/tex]
or, [tex]y =18[/tex] [ by cross multiplication]
Again,
[tex]tan30^\theta = \frac{9}{x}[/tex]
or, [tex]\frac{1}{\sqrt{3} } = \frac{9}{x}[/tex]
or, [tex]x = 9\sqrt{3}[/tex] [ by cross multiplication]
Hence,
The value of x and y is 9√3 unit and 18 unit respectively.