This is what you should be looking at now:
(Kind of messy, but you get the idea, haha.)
The line down the middle is the Height (represented by h). The distance from the bottom to the top - that's what you have to find.
Also, note that the base is 15. That means that both halves have a base of 7.5.
Since we have all our angles and measures now, we can easily find the h by working one side of the split triangle. Turn it into a triangle of its own:
It has a right angle, 90, and its B angle of 49. This means that the A angle is now 41.
Now we can use the formula a^2 + b^2 = c^2 to get h.
10^2 + 7.5^2 = h^2.
156.25 = h^2.
h = 12.5. And that's your answer.