Given:
LMN is an equilateral triangle.
LM = LN = MN = 12 cm
To find:
The height of the triangle h.
Solution:
In a right angle triangle,
[tex]\sin \theta=\dfrac{Opposite}{Hypotenuse}[/tex]
[tex]\sin (60^\circ)=\dfrac{h}{12}[/tex]
[tex]\dfrac{\sqrt{3}}{2}=\dfrac{h}{12}[/tex]
Multiply both sides by 12.
[tex]\dfrac{\sqrt{3}}{2}\times 12=\dfrac{h}{12}\times 12[/tex]
[tex]6\sqrt{3}=h[/tex]
Therefore, the height of the triangle is [tex]6\sqrt{3}[/tex] cm.
