First you'll want to draw your triangles (2 right triangles with the pole running through the middle). The angles you know are 72 degrees on the bottom left corner and 48 degrees on the bottom right corner. With this, you can figure out what the remaining angles are.
Angles of a triangle add up to 180 degrees so the missing top angle for the first triangle is 18 degrees (180 - (90 + 72)) and the missing top angle for the second triangle is 42 degrees.
You can now set up a ratio since angles are directly proportional to their opposite side. You know that the bottom is 20 meters. This means that 18/(18+42) = x/20, which simplifies to x = 6. This means the bottom of the first triangle is 6 meters, and it follows that the bottom of the second triangle is 12 meters (although you don't really need this information).
Now comes the trig. You need to figure out the length of the hypotenuse of one of the triangles so that you can use the Pythagorean Theorem to figure out the height of the pole. You can set up tan(72) = (6/x) - tangent is opposite over adjacent - which simplifies to x = 6/tan(72). You can plug this into your calculator (make sure you're in degrees mode) and you'll get x = 5.4024. This is the length of your hypotenuse.
Now plug this value into the Pythagorean Theorem (a^2+b^2=c^2) to get 6^2 + b^2 = (5.4024)^2 = c^2, c^2 = 65.1862, and c is approximately 8.0738!
8.0738 meters tall.
