



 
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  


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