Each edge of the following cube is 1 and C is a point on the edge.
What would the height of triangle be in this case , how would you measure it?
Each edge of the following cube is 1 and C is a point on the edge.
What would the height of triangle be in this case , how would you measure it?
Assuming you mean "height" as "altitude passing through point $C$". You might want to clarify if this is not correct:
The height of the triangle is just the distance from $C$ to the line $AB$. Cutting the cube perpendicular to $AB$ and containing point $C$, we find a right angled triangle with both legs of length $1$, and the height of the triangle as its hypotenuse. So the height of the triangle is $\sqrt{1^2+1^2}=\sqrt 2$
It's also good to realize that the height doesn't change depending on where $C$ is, so you can just arbitrarily move it to one vertex and take the height along the corresponding face.
Picture: