Calculate the height of a distant object using estimated angles from two different points. I knew how to do this long ago, found the exact problem in my old trig book, but I can't seem to work it out.

Say I'm at an unknown distance from a mountain, called point P, and I estimate the angle of elevation to the top of the mountain is 13.5 degrees. Then I move to point N, which is 100 meters closer to the mountain, and I estimate the angle of elevation to be 14.8 degrees. What is the height of the mountain?

I remember this being enough information to solve both triangles, but without the distance to the mountain, or the height of the mountain, I'm at a loss.  Hint's would be appreciated.
Or...

Use the Law of Sines to find the longest side in the triangle with the 100 m side (you know all the angles).

This longest side is also the hypotenuse of a another, right angle triangle where you know the angle opposite the height you want...
Let $O$ and $M$ the base point and the tip of the mountain, respectively. Then
$$NM=100\cdot\frac{\sin13.5}{\sin1.3},$$
and $OM$ is the height of the mountain, where
$$OM=NM\cdot\sin14.8\approx262.854.$$
Note that the input of the sine is in degrees.