Now that you’ve seen how necessary math is in our daily lives, let’s try to solve this practical problem using the above formula to get an answer (and a mind-set) to solve even more problems later.
What if we had this situation:
Lightning struck a tree, causing it to break and crash to the
ground. The tree broke off 12 feet above the ground and the
broken part was 20 feet long. If the broken tree formed a right
triangle, could we be able to determine how far away the tip of the fallen tree is?
Of course we can! Let’s find x, which is variable “b”.
Recall the Pythagorean Theorem:
a squared + b squared = c squared
Replace the variables with any values we can see from the problem: a = 12 ft, b is unknown, and c is the hypotenuse and equals 20 ft.
- 12 squared + b squared = 20 squared
- 144 + b squared = 400
subtract 144 from both sides to get b squared all by itself
- b squared = 400 – 144
- b squared = 256
take the square root of both sides
- b = 16 ft
We did it!
The tip of the broken tree is 16 feet from the base.
Retrieved and adapted from: https://www.risd.k12.nm.us/problems/Problem93.pdf