Answer:
10.4 cm
Step-by-step explanation:
Looking at the triangle in the attached pic, we can see that the right, smaller triangle is a right triangle on which we can apply the pythagorean theorem to solve for the height, h.
Pythagorean theorem tells us [tex]c^2=a^2+b^2[/tex] where c is the hypotenuse (12 in our case) and a & b are the two legs (6 and h are the respective lengths).
So let's solve for h:
[tex]c^2=a^2+b^2\\12^2=6^2+h^2\\144=36+h^2\\144-35=h^2\\108=h^2\\h=\sqrt{108} \\h=10.4[/tex]
