Tuesday, March 18, 2008
Pythagorean Theorem: Problem A
You are locked out of your house and the only open window is on the second floor, 25 feet above the ground. You need to borrow a ladder from one of your neighbors. There's a bush along the edge of the house, so you'll have to place the ladder 10 feet from the house. What length of ladder do you need to reach the window?In this picture I made of the problem, the bushes were removed, but we still have to solve the problem.
To find the missing side, you have to run through the Pythagorean Theorem and find out what the missing side is.
a = 25 feet
b = 10 feet
c = ?
a² + b² = c²
25² + 10² = c²
625 + 100 = c²
725 = c²
of 725 = c²
Now we make the fractional then decimal form of the square root of 725.
Since 26 is 1 unit larger than 25, we have to square the number 26 and subtract that number from 725 (725 - 676).
27 x 27 = 729 - we can't use this because its larger than 725
26 x 26 = 676
So, back to the subtraction:
725 - 676 = 49
49 becomes the numerator of the fraction after 26.
To find the denominator, you have to add 26 with the number after it, which is 27
26 + 27 = 53.
The answer to 725 squared = 26 49/53
But we aren't done yet, we have to make it into a decimal form. *opens calculator*
26 49/53 = 26.924
26.924 = C
26.924² = c²
So the missing side length of the picture above is 26.924.
Another way we could have found the fraction after 26 is doing the "mullet" strategy.
D = Denominator of fraction after 26