Note: Consider the below figure attached with this question.
Given:
[tex]a=3\sqrt{3}[/tex]
To find:
The value of b.
Solution:
In a right angled triangle,
[tex]\tan \theta = \dfrac{Perpendicular}{Base}[/tex]
For the given right angled triangle,
[tex]\tan \theta = \dfrac{a}{b}[/tex]
[tex]\tan (30^\circ) = \dfrac{3\sqrt{3}}{b}[/tex]
[tex]\dfrac{1}{\sqrt{3}} = \dfrac{3\sqrt{3}}{b}[/tex]
On cross multiplication, we get
[tex]1\times b=3\sqrt{3}\times \sqrt{3}[/tex]
[tex]b=3(3)[/tex]
[tex]b=9[/tex]
Therefore, the value of b is 9.
