## anonymous one year ago Use the triangle at the right. Find the length of the missing side. Show your work Did i do the first one right? I don't want to do the second one wrong too. 1.a = 16, b = 63 2. b = 2.1, c = 2.9 16^2 =256, 63^2=3,969 256+3969 = 4225 now we need to find the square root by separating the 4225 into two separate numbers square root of 42 is 6 now find the largest root in 42. Which is 36. 6*6 = 36 and the square of 25 is 5 add the roots This give me the answer for c length. 6 and 5 is 65. a=256 b=3969 and c = 65

1. SolomonZelman

Do you have a picture or other description of the triangle you are dealing with in problem 1 and/or problem 2?

2. anonymous

yup you need a picture

3. anonymous

The picture probably wouldn't help it's just a right triangle but okay

4. anonymous

@SolomonZelman

5. SolomonZelman

this picture will definitely help, because I would have thought that b is the hypotenuse

6. SolomonZelman

i mean in question 1 i would have thought so, but this picture gives me that c=hypotenuse in both cases, and I know it is a right triangle

7. anonymous

Alright.

8. SolomonZelman

I want to correct you though. The set up is a little different, that is 1. Here is the rule. A right triangle with sides a, b, c (where the hypotenuse is side c), must satisfy the following statement: a²+b²=c²

9. SolomonZelman

this statement is known as the pythagorean theorem.

10. SolomonZelman

Now, you are given your two smaller legs a and b are 16 and 63 (respectively). And you are missing the hypotenuse, so this is what you would do. (16)² + (63)² = c²

11. SolomonZelman

then you simplify the left hand side, and solve for c (just by talking the square root of both sides)

12. anonymous

So i had to square c?

13. anonymous

Take the square root of a and b?

14. SolomonZelman

(16)² + (63)² = c² 4225 = c² then do this: $$\sqrt{4225}$$ = $$\sqrt{{\rm c}^2}$$

15. SolomonZelman

this way you are able to solve for c. (normally the square root will give you the ±, as you know, but in this case since distance or sidelength can not be negative, you diregard any negative solutions)

16. anonymous

Alright. is c 65? @SolomonZelman

17. SolomonZelman

yes

18. anonymous

Did i do the problem right?

19. SolomonZelman

i wrote it all out and still doesn't take that much space and time..... ok, now question 2...

20. anonymous

Kay.

21. SolomonZelman

oh, I deleted that.... ------------------ a²+b²=c² 16²+63²=c² 4225=c² √4225 = √c² c=65 ------------ reposted it.

22. SolomonZelman

ok, in question 2, you are given c=2.9 b=2.1

23. SolomonZelman

can you plug in this information into the a²+b²=c² ?

24. anonymous

Sure a^2+ b^2=c^2

25. SolomonZelman

but, you are given the c and b, so you can g ahead and plug in 2.9 for c, and 2.1 for b.

26. anonymous

2.9^2 + 2.1^2

27. SolomonZelman

no,

28. SolomonZelman

The pythagorean theorem is: a²+b²=c² where c is the hypotenuse and a & b are two legs. you are given that your c (which is hypotenuse as well) is 2.9 and you are given that your b is 2.1 (your missing side is a)

29. anonymous

Alright

30. SolomonZelman

31. anonymous

2.9^+2.1=c^2

32. SolomonZelman

your c is given, but a is not

33. SolomonZelman

it is like this: a² + (2.1)² = (2.9)²

34. anonymous

Oh sorry.

35. SolomonZelman

it's ok...

36. anonymous

2.9^+2.1=c^2

37. SolomonZelman

a² + (2.1)² = (2.9)²

38. anonymous

Wifi is bad okay a^2 +(2.1)^2 =( 2.9)^2

39. SolomonZelman

because you are given: c=2.9 b=2.1 so, the missing side is a. Our theorem is: a² + b² = c² so lets plug in everything plugging 2.9 for c plugging 2.1 for b you get: a² + (2.1)² = (2.9)²

40. SolomonZelman

ok now solve for a

41. anonymous

Alright one moment

42. anonymous

Do i add the c value or divide or do it the same thing i did in my last problem.

43. anonymous

@SolomonZelman you there?

44. SolomonZelman

you first calculate the values of (2.1)² and (2.9)²

45. anonymous

Alright.

46. anonymous

4.41= 8.41. Do i subtract next?

47. SolomonZelman

a² + (2.1)² = (2.9)² without a calculator: 21•20=420 21•21=420+21=441 so 2.1² = 4.41 30•30=900 30•29=900-30=870 29•29=870-29=841 so 2.9²=8.41

48. SolomonZelman

just demonstrating another technique.

49. SolomonZelman

anyway a² + (2.1)² = (2.9)² a² + 4.41 = 8.41 yes you subtract 4.41 from both sides

50. anonymous

Okay.

51. SolomonZelman

a² + 4.41 $$\small \color{red}{-4.41}$$= 8.41$$\small \color{red}{-4.41}$$

52. SolomonZelman

and from this u get?

53. anonymous

4.00

54. SolomonZelman

yes, or just 4 :)

55. SolomonZelman

so, a²=4 correct?

56. anonymous

Yeah it looks correct i don't think it can be factored anymore

57. SolomonZelman

no, there is no factoring here:) so we got a²=4 what do you think your next (and final) step is?

58. anonymous

putting them together like 2.1^2+2.9^2= 4^2

59. SolomonZelman

u just take the square root of both sides $$a^2=4$$ $$\color{red}{\sqrt{\color{black}{a^2}}}=\color{red}{\sqrt{\color{black}{4} }}$$

60. SolomonZelman

a = ?

61. anonymous

4^2?

62. SolomonZelman

a square root of a 4 is?

63. anonymous

2?

64. SolomonZelman

yes so a=2

65. anonymous

Alright is there anything else?

66. SolomonZelman

no, you found the missing side in both of the problems.

67. anonymous

Alright thanks for your help :)

68. SolomonZelman

yw