Another trigonometry bearing question

Question

[2 marks] A flagpole broke in a storm. 7 metres are still sticking straight out of the ground, where it snapped, but the remaining piece has hinged over and touches the ground at a point 24 metres away horizontally. How tall was the flagpole before it broke?

Plrase tell me how to work this out

Answer 1

Since the flagpole (we assume) makes a right angle with the ground we have right triangle with a height of 7 m and a base of 24 m. We can use the Pythagorean Theorem to find the length of the hypotenuse.

z² = x² + y²

Where x, y are the base/height.

This also happens to be a Pythagorean Triple so we can also take the shortcut and know the hypotenuse length is 25 m.

Add that hypotenuse (25 m) to what was left standing (7 m) and you get a total height of 32 m.

Answer 2

This is a Pythagorean Theorem problem. The sides are 7 and 24, you are solving for the hypotenuse.

7²+24²=c²

49+576=c²

625=c² Take the square root of both sides

c=25 m