Question

you might need: calculators
a flagpole broke in a storm. 7 meters 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 meters away horizontally.
how tall was the flagpole before it broke?
□ meters

Explanation:

Step1: Identify the right triangle

The flagpole forms a right triangle with the ground, where the vertical part is 7 m, the horizontal distance is 24 m, and the broken part is the hypotenuse. Let the length of the broken part be \( c \).
Using the Pythagorean theorem \( a^2 + b^2 = c^2 \), where \( a = 7 \) and \( b = 24 \).

$$ c = \sqrt{7^2 + 24^2} $$

Step2: Calculate the hypotenuse

First, calculate \( 7^2 = 49 \) and \( 24^2 = 576 \). Then sum them: \( 49 + 576 = 625 \). Take the square root: \( \sqrt{625} = 25 \). So the broken part is 25 m.

Step3: Find the total height

The total height of the flagpole before breaking is the sum of the vertical part and the broken part: \( 7 + 25 = 32 \).

Answer:

32