Astraight pole which was vertical is broken 36 feet from the ground, and the top part comes down diagonally from the break until it touches the ground 27 feet from the bottom of the pole. how many feet tall was the pole?

So to answer this, you need to use pythagoras' theorem (a² + b² = c²). So its kinda like a triangle with the hypotenuse being the angled part of the pole that fell. 

if c is the hypotenuse then you must sub into the formula
36² + 27² = c²
1296 + 729 = c²
2025 = c²
so to find c, you must find the square root of 2025
√2025 = 45

however the question is asking what the full length of the pole was before it broke so that would be the part that fell (45ft) + the part remaining (36ft), so the answer is 81ft