Let's plot 4 points.
Draw a building
Point A is the location (on the ground) of the 1st spot you found the 1st measurement (the 32º angle)
Point B is the location (on the ground closer to the building than the 1st spot) of the 2nd spot you found the 2nd measurement (the 53º angle)
Point C is the location at the top of the building.
Connect A to B, A to C, and B to C - making an obtuse triangle
Label AB - 50m
Label CD - H (represents Height of Building - what you are trying to find out)
NOW, extend AB to where it meets the building.
Label the point where AB extended meets the building D
Label BD - X (we don't know how far this is --- yet)
If you connect the 'dots', you should have:
• C (top of building)
h -- height of building
•A (32º) -----------50m---------------- • B (53º)---------- x ------------ • D (base of building)
We first need to solve for x.
Using the rules of tangents -opposite over adjacent- and using the base of the building as a right angle (unless you're in Pisa), we have:
tan(32º)= h AND tan(53º)= h
Solving for h for both equations, we have:
h = tan(32º)(50+x) AND h = x tan(53º)
Using subitution [sic], we have:
tan(32º)(50+x) = x tan(53º)
Solve for x. Once you find x, use either equation for h (I'd suggest h = x tan(53º) )