Answer:
[tex]x=6\sqrt{3}[/tex] units.
Step-by-step explanation:
It is given that shorter leg of a 30°-60°-90° triangle is 6.
In a triangle larger interior angle has larger opposite side and vice versa.
The length of shortest leg is 6 units it means it is opposite to the angle 30°.
Let the length of second leg be x.
In a right angle triangle,
[tex]\tan \theta =\dfrac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\tan (30^\circ) =\dfrac{6}{x}}[/tex]
[tex]\dfrac{1}{\sqrt{3}}=\dfrac{6}{x}}[/tex]
On cross multiplication, we get
[tex]x=6\sqrt{3}[/tex]
Hence, the length of the other leg is [tex]x=6\sqrt{3}[/tex] units.
