## Emily778 2 years ago Find the length of the missing side.

1. Emily778

2. Emily778

3. FutureMathProfessor

|dw:1370548165122:dw|

4. FutureMathProfessor

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5. Jhannybean

oh my goodness. lol.

6. mitodoteira

$a ^{2}+b ^{2}=c ^{2}$ $8 ^{2}+15 ^{2}=x ^{2}$ $64+225=x ^{2}$ $x ^{2}=289$ $x=\sqrt{289}$ $x=17$

7. Emily778

8. mitodoteira

Okay

9. Jhannybean

Aww that's not being a good sport.

10. arafatx

The question didn't ask for x, should be 17^2 or 289

11. mitodoteira

Emily, what is the other question?

12. Emily778

In triangle ABC, <A is a right angle and m<B= 45 degrees. Find BC. If your answer is not and integer, leave in simplest form. @mitodoteira

13. Jhannybean

the length of the missing side would be what @arafatx mentioned. You can always plug it back in to the pythagorean identity to check your answer. a^2 +b^2 = c^2 (15)^2 + (8)^2 = (sqrt (289))^2 225 + 64 = 289

14. Emily778

is that for the second one?

15. Jhannybean

and for that question,you have a 45-45-90 triangle, therefore your proportions are 1:1:1*sqrt(2) By that i mean both of your base legs are the same and to find the hypotenuse you're going to multiply your base leg * sqrt(2)

16. Jhannybean

b1 = 12, b2 = 12, hypotenuse = b1*sqrt(2)

17. mitodoteira

Since <B is 45º and and <A is 90º, <C is (180-(90+45)=45) 45º. Thus, the triangle is isosceles. $a ^{2}+b ^{2}=c ^{2}$ $12 ^{2}+12 ^{2}=x ^{2}$ $2•144=x ^{2}$ $x ^{2}=288$ $x=\sqrt{288}$ $x=12\sqrt{2}$ $x \approx 16.97056 \approx 17$

18. Emily778

you guys are giving me 2 different answers. Which is it?

19. mitodoteira

12*sqrt(2) is about equal to 17

20. Jhannybean

@mitodoteira c^2 = a^2 + b^2 take x = 17, c=x (17)^2 = (12)^2 + (12)^2 289 = 288 nope.

21. mitodoteira

That's because I'm rounding. The actual answer is irrational. If you look at my answer, I gave the answer to a few decimal places as well.

22. Jhannybean

whereas we take c = 12sqrt(2) c^2= a^2 + b^2 (12sqrt(2))^2 = (12)^2 + (12)^2 288 = 288 You DO NOT round when finding lengths.

23. mitodoteira

I gave the true answer, as well as the rounded one in case she needed it for something (I was often asked to give the answer to n decimal places instead of the exact answer).

24. Jhannybean

the "true" answer is 12* sqrt(2) according to the 45-45-90 degree triangle.

25. mitodoteira

Yes, it is. I don't see what the problem is.

26. Jhannybean

Emily778 You've already chosen the best response. 0 In triangle ABC, <A is a right angle and m<B= 45 degrees. Find BC. If your answer is not and integer, leave in simplest form.

27. Jhannybean

"if the answer is not an integer, leave it in simplest form" and therefore the simplest form is 12*sqrt(2)

28. mitodoteira

What I said was 'x=12*sqrt(2), x APPROXIMATELY EQUALS 16.97056 approx 17' I am new to this community. Most others I have been to welcome extra information.

29. Jhannybean

the approximation then would be longer than 16.97056. you'd have to include the whole number approximation, not rounding up to 17.

30. Luigi0210

If it's suppose to be in exact or simplified form then leave it as radicals, fractions etc. If it asks for estimation, nearest number, or approximation then that's when you round up and change the radical to a number

31. Luigi0210

32. ganeshie8

yeah, simplest form = $$12\sqrt{2}$$

33. Luigi0210

Thank you Gane