Answer :
Answer:
The value of x is 9.
The value of y is 18.
Step-by-step explanation:
The given triangle is a right angled triangle.
We have: [tex]$ tan(x) = \frac{opp}{adj} $[/tex]
Therefore, [tex]$ tan(30) = \frac{x}{9\sqrt{3}} $[/tex]
Since, [tex]$ tan(30) = \frac{1}{\sqrt{3}} $[/tex]
Therefore, we have:
[tex]$ \frac{1}{\sqrt{3}} = \frac{x}{9\sqrt{3}} $[/tex]
[tex]$ \implies x = 9 $[/tex]
Now, 'y' is the hypotenuse.
Use Pythagoras theorem, we have [tex]$ x^2 + (9\sqrt{3}})^2 = y^2 $[/tex]
Substituting x = 9, we get:
81 + 81(3) = y²
[tex]$ \implies y^2 = 81 + 243 $[/tex]
[tex]$ \implies y^2 = 324 $[/tex]
[tex]$ \therefore y = 18 $[/tex]
Hence, the value of y = 18.