The telephone pole is 7.746 meters
First, I draw a right triangle where one leg (leg = sides forming right angle) is x meters, the height of the telephone pole and the other leg is 2 meters - representing where the pigeon sat before flying up the pole. The hypotenuse, is 8 meters long - connecting where the pigeon sat to the top of the telephone pole.
I can use the Pythagorean theorem to solve for b, the high of the telephone pole. The Pythagorean theorem is: a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse. I can now plug in the numbers: (2)^2 + x^2 = (8)^2
4 + x = 64
x^2 = 60
x = sqrt(60) = 7.746 meters
The height of the telephone pole is around 7.746 meters