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,
![\sin \theta=\dfrac{Opposite}{Hypotenuse}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D%5Cdfrac%7BOpposite%7D%7BHypotenuse%7D)
![\sin (60^\circ)=\dfrac{h}{12}](https://tex.z-dn.net/?f=%5Csin%20%2860%5E%5Ccirc%29%3D%5Cdfrac%7Bh%7D%7B12%7D)
![\dfrac{\sqrt{3}}{2}=\dfrac{h}{12}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%3D%5Cdfrac%7Bh%7D%7B12%7D)
Multiply both sides by 12.
![\dfrac{\sqrt{3}}{2}\times 12=\dfrac{h}{12}\times 12](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5Ctimes%2012%3D%5Cdfrac%7Bh%7D%7B12%7D%5Ctimes%2012)
![6\sqrt{3}=h](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7D%3Dh)
Therefore, the height of the triangle is
cm.
Do you need this solved in a specific way? Solving for y you get 3/2
hmmmm i think there is another part of this
Hello!! Actually I got A x = 2, y = 12.
Whenever you plug them in, 2(2) + 3(12) = 40
-2(2) + 2(12) = 20
It worked for me this way, I hope this is the right answer. Have a great day!