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# Pythagoras Theorem

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### Pythagoras Theorem

1. 1. use the Pythagorean Theorem
2. 2. leg hypotenuse right angle legIt is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse.
3. 3. In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a2 + b2 = c2. Note: The hypotenuse, c, is always the longest side.
4. 4. 122 + 162 = c2 144 + 256 = c2 400 = c2Take the square root of both sides. 400 = c 2 20 = c
5. 5. 42 + b2 = 102 16 + b2 = 100 Solve for b.16 - 16 + b2 = 100 - 16 b2 = 84 b = 84 2 b = 9.17
6. 6. a2 + 72 = 102a2 + 49 = 100Solve for a.a2 = 100 - 49 a2 = 51 a = 51 2 a = 7.14
7. 7. 73 Which side is the biggest?The square root of 73 (= 8.5)! This must be the hypotenuse (c). Plug your information into the Pythagorean Theorem. It doesn’t matter which number is a or b.
8. 8. 73 73 9 + 64 = 73 73 = 73Since this is true, the triangle is a right triangle!! If it was not true, it would not be a right triangle.
9. 9. Charming Prince Castle Rapunzel
10. 10. Rapunzel and her Prince charming hada problem. Rapunzel cut her hair! NowPrince charming can’t reach her. What ishe going to do???
11. 11. Well lucky for Rapunzel, Prince charming is a rich Engineer. Prince charming knows that he just needs the measurements of the building and the ladder.Can you help him find the height of the castle? (Castle has 10 floors and each floor is 100 feet in height)
12. 12. Now we need to know how long is Prince Charming’s ladder. Each step is 110 feet from last one and 11 steps in total.
13. 13. How far from the bottom of the castledoes Prince charming need to put hisladder?
14. 14. Height of ladder i.e. 11 x 110 = 1210 feet.Height of castle i.e. 10 x 100 = 1000 feet.
15. 15. Lets make it a right angle triangle A= Castle C= ladder B= ?
16. 16. Put it in the formula: A2 + B2 = C2 and find the distance where the ladder should be kept so that the Charming Prince could reach Rapunzel.
17. 17. The ladder should be kept 681.25 feetaway.
18. 18. Any queries and questions are mostwelcome