Pythagorean+Theorem

  //Pythagorean Theorem// - describes the relationship of the lenghths of the sides of a right triangle. //Real World Promb//lems - A fire truck parks beside a building such that the base of the ladder is 16ft from the building.The fire truck extends its ladder 30 ft as shown at the left .How high is the top of the ladder above the ground? //Define// -let b= height(in feet) of the ladder from a point 10Ft above the ground. //Relate// - The triangle formed is a right triangle.Use the Pythagorean Theorem. //Write// -a^2+b^2=c^2 16^2+b^2=30^2 //substitute// 256+b^2=900 //simplify// b^2=644 //subtract 256 from each side// //take square root of each side and u get// b=25.4 (MATH TEXTBOOK)

Key Terms: 1.Hypotenuse - the side opposite the right angle in a right triangle. It is the longest side in the triangle. 2.Leg - each of the sides that form the right angle of a right triangle. 3.Converse - The statement obtained by reversing the if and then parts of an if-then statement. 4.Conclusion -In a conditional, the part following then. 5. (MATH TEXTBOOK)

4 Examples: =62 + 82= Simplifying the squares gives: h2 36 + 64and then: h2 = 100
 * 1)  [[image:http://www.worsleyschool.net/science/files/pythagoras/pythprobpic1.JPG width="133" height="152"]] In the right triangle at the left, we know that: ** h2 **

2.  3. Simplifying the squares gives: h2 49 + 100 h2 =149 This square root is not perfect. A calculator gives:** h **= 12.2 ||
 * [[image:http://www.worsleyschool.net/science/files/pythagoras/pythprobpic3.JPG width="143" height="154" align="center"]] || In this example, the missing side is **not** the long one. But the theorem still works,//as long as you start with the hypotenuse://**152 = x2 + 92**Simplifying the squares gives: 225 = x2 + 81and then: 225 - 81 = x2 144 = x2 **12 = x ** ||
 * [[image:http://www.worsleyschool.net/science/files/pythagoras/pythprobpic2.JPG width="143" height="158" align="center"]] || In the right triangle at the left, we know that: ** h2 =72 + 102=**

4.
 * [[image:http://www.worsleyschool.net/science/files/pythagoras/pythprobpic4.JPG width="145" height="160" align="center"]] || Again, the missing side is **not** the long one. But we start with the hypotenuse: **182 = x2 + 112**Simplifying the squares gives: 324 = x2 + 121and then: 324 - 121 = x2 203 = x2 **14.2 = x ** ||

Word Promblem: Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the //nearest tenth// of a mile, they must travel to return to their starting point? **Choose:** 8.4       9.5       9.4  13.1

2 ADDITIONAL LINKS:[|pythagorean theorem],|pythagorean theorem infomation