Phoenix,

Hi Phoenix,

You didn't say which side is the base. If the 105^o angle is the apex then the diagram is approximately

AD is perpendicular to BC so |AD| = h is the height of the triangle. I let |DC| = x and then |BD| = 2√2 - x. You can use a trig function to relate h and x in two ways, one by using the 45^o angle and the second by using the 30^o angle. This gives you two linear equations in h and x which you can solve for h.

If the 105^o angle is not the apex then D will be on an extension of the base. In this case let x be the distance from D to the nearest vertex on the base and the the distance from D to the furthest vertex will be 2√2 + x. A similar use of trig functions will produce equations that can be solved for h.

Penny