Triangle Problem

Question

A metal flagpole is perpendicular to level ground. In a bad storm, the flagpole broke at a certain point with the top part tipping over like a hinge and the tip hitting the ground at a point 20m from the base. It was repaired, but then another storm came and the flagpole broke again. This time the break was at a point 5m lower than the first time, and the pole's tip hit the ground 30m from the base of the pole. What is the eight of the flagpole?

Answer 1

Draw the geometric diagram:

From the triangle OAC:

Using the pythagoras theorem

(h-x)²= 20²+x²             ....... (1)

From the triangle OBD:

Using the pythagoras theorem

(h-x+5)²= 30²+(x-5)²    ....... (2)

Solve the equations (1) and (2)

h = 50 m

x = 21 m

Therefore, the height of the pole is 50 m