LFP+Mathematical+Reflections,+p+40


 * __Wednesday, October 28th, 2009__**
 * M.I.**

** Mathematical Reflection #3 (pg.40) **
 * THE DIMENSIONS OF A RIGHT TRIANGLE CAN BE DETERMINED WITH LIMITED INFORMATION. **
 * __ Essential Question #3: __**** How can I find the perimeter of a right triangle? **
 * 1A.) Suppose you are given the lengths of the legs of a right triangle. Describe how you can find the length of the hypotenuse.**

Ans. : If the lengths of the two legs are given (a and b), to find the hypotenuse (c), we use the “Pythagorean Theorem”:

c2 = a2 + b2  c = Ö (a2 + b2)


 * 1B.) Suppose you are given the lengths of one leg and the hypotenuse of a right triangle. Describe how you can find the length of the other leg.**

Ans. 8 2 = a 2 + 5 2 64 = a 2 + 25 64 – 25 = a 2 39 = a 2 (Now you have to use the square root sign on the 39 to find a 2 ) Ö 39 = a 2 * 6.2 = a *
 * 2.) Describe how you can use the Pythagorean theorem to find the distance between two dots on a sheet of paper without measuring.**

Ans. To find the distance between two dots on a dotted centimeter grid, you should name the two dots. Lets say C and D. Next make a triangle with line CD as the hypotenuse. We name the other point made X. Pretending that line CX is 4 cm for it is crossing through 4 points. Same with line DX, except the fact that it has a 3 cm line for it crosses through 3 dots. Using the Pythagorean theorem we can find the hypotenuse because we know the length of the 2 legs. EX.  C 2  = a 2  + b 2  C 2 = 4 2 + 3 2 C 2  = 16 + 9 C 2 = 25 C 2  = Ö <span style="font-size: 12pt; color: rgb(102, 0, 102); font-weight: normal">(25) <span style="font-size: 12pt; color: rgb(102, 0, 102)">* C = 5 <span style="font-size: 12pt; color: rgb(102, 0, 102)">* <span style="font-size: 12pt; color: rgb(102, 0, 102)"> <span style="color: rgb(51, 102, 255)">Ans. We can determine whether a triangle is a right triangle by seeing if the Pythagorean theorem applies to the triangle. The square of the longest side, the hypotenuse, should equal to the sum of the squares on the other side, its legs. The Pythagorean theorem only works on right triangles. <span style="font-size: 12pt; color: rgb(51, 102, 255); font-weight: normal">EX. C <span style="font-size: 12pt; color: rgb(51, 102, 255)">2 <span style="font-size: 12pt; color: rgb(51, 102, 255); font-weight: normal"> = a <span style="font-size: 12pt; color: rgb(51, 102, 255)">2 <span style="font-size: 12pt; color: rgb(51, 102, 255); font-weight: normal"> + b <span style="font-size: 12pt; color: rgb(51, 102, 255)">2 <span style="font-size: 12pt; color: rgb(51, 102, 255); font-weight: normal"> C <span style="font-size: 12pt; color: rgb(102, 0, 102)">2 = 6 <span style="font-size: 12pt; color: rgb(102, 0, 102)">2 + 3 <span style="font-size: 12pt; color: rgb(102, 0, 102)">2 <span style="font-size: 12pt; color: rgb(51, 102, 255); font-weight: normal">C <span style="font-size: 12pt; color: rgb(51, 102, 255)">2 <span style="font-size: 12pt; color: rgb(51, 102, 255); font-weight: normal"> = 36 + 9 C <span style="font-size: 12pt; color: rgb(102, 0, 102)">2 = 45 <span style="font-size: 12pt; color: rgb(51, 102, 255); font-weight: normal">C <span style="font-size: 12pt; color: rgb(51, 102, 255)">2 <span style="font-size: 12pt; color: rgb(51, 102, 255); font-weight: normal"> = <span style="font-size: 12pt; font-family: Symbol; color: rgb(51, 102, 255)">Ö <span style="font-size: 12pt; color: rgb(51, 102, 255); font-weight: normal">45 In the chapters 3.1, 3.2, 3.3, and 3.4, I have learned how to use the “Pythagorean theorem”. The Pythagorean theorem can only be used when dealing with right triangles. It lets us know the measurement of the hypotenuse or legs of a right triangle. The formula is: c = a + b. In investigation 3.1, I learned how to apply the Pythagorean theorem on right triangles. I learned the legs ´ itself + its legs ´ itself = the hypotenuse (c = a + b). In investigation 3.2, I started actually using the formula. Investigation 3.3, got me used to the formula by doing some more practice problems. In investigation 3.4, the problems got a bit trickier. For example, some questions were asking about how to find the length of a leg instead of the hypotenuse by using the Pythagorean theorem. We would have to add up the leg squared length that was given to the hypotenuse squared which gave us the length of the missing leg. The Pythagorean theorem is useful in life because all buildings need it to be formed. Therefore, we learned the Pythagorean theorem in chapter 3!
 * 3.) How can you determine whether a triangle is a right triangle if you know only the lengths of tits three sides? **
 * __ My Summary: __**

<span style="font-size: 12pt; color: rgb(51, 102, 255)"> <span style="font-size: 12pt; color: rgb(51, 102, 255); font-weight: normal">