Given:
A figure of a right triangle.
To find:
The value of x and value of y.
Solution:
In a right angle triangle,
[tex]\sin \theta = \dfrac{Opposite}{Hypotenuse}[/tex]
[tex]\cos \theta = \dfrac{Base}{Hypotenuse}[/tex]
In the given triangle,
[tex]\sin (60^\circ)=\dfrac{x}{6}[/tex]
[tex]\dfrac{\sqrt{3}}{2}=\dfrac{x}{6}[/tex]
[tex]\dfrac{\sqrt{3}}{2}\times 6=x[/tex]
[tex]3\sqrt{3}=x[/tex]
And,
[tex]\cos (60^\circ)=\dfrac{y}{6}[/tex]
[tex]\dfrac{1}{2}=\dfrac{y}{6}[/tex]
[tex]\dfrac{1}{2}\times 6=y[/tex]
[tex]3=y[/tex]
Therefore, the value of x is [tex]3\sqrt{3}[/tex] and the value of y is 3.
