How do I solve this word problem

A building has a flagpole on top of its roof. From a point on the ground that is 100 m away from the building, the angle of elevation to the bottom of the flagpole is 18 degrees and the angle to the top of the flagpole is 31 degrees. How tall is the flagpole to the nearest tenth of a meter?

Thank you so much!

your answer is:

(100 m) x sin(31) - (100 m) x sin(18) = (100 m) x (sin(31) - sin(18))

I don't have a calculator on me, but if you run that it will give you the right answer. This is how I came up with it:

I know the distance away from the flagpole to be 100 m. I know the angle to the top and the angle to the bottom. What I need is the vertical height of the flagpole. I can calculate the vertical height to the top of the pole from the ground using the 31 degree angle and my 100 m distance, and I can calculate the vertical height to the bottom of the flag pole from the ground using 18 degrees and my 100 m distance. The difference b/w the two is the height of the flag pole. Remember that the sine of an angle is the ratio of the length opposite it to the length adjacent to it. in our case, the opposite is the vertical height, and the adjacent is the 100 m horizontal measurement.

Hope this helps.