## Sandiego19 3 years ago Can Someone Please Explain Me In Steps How To Solve For a and b ?

1. Sandiego19

|dw:1337230739451:dw|

2. Sandiego19

the numbers are 29, 20, 21

3. sritama

is it a right angled triangle ??/

4. nickymarden

all you have to do is use similarity. see what angles are the same.

5. nickymarden

and then use proportions. As you can see, the sides 29 and b are proportional, because the hypotenuse of the two similar triangles. same goes ofr the other sides. like this: actually it's 29/b=20/21=21/a for b: 29/b=20/21 b=(20/21)29 for a: 21/a=20/21 a=(20/21)21 get it?

6. Sandiego19

Yes Thanks Alot :)

7. jim_thompson5910

you have the right idea nickymarden, but you have the wrong values It should be a/20 = 20/21 which after solving for 'a' gives you a = 400/21 and b/20 = 29/21 which gives you b = 580/21

8. nickymarden

haha, yeah you're right. sorry. it's 2 am here, can't blame me..

9. jim_thompson5910

But I love this way better. I was set to use the pythagorean theorem until you wrote that lol

10. SmoothMath

I don't think there is any way to. Is there, Jim?

11. Sandiego19

SO , A = 400/21 And B = 580/21

12. nickymarden

yes love, i'm sorry. @jim_thompson5910 is right :)

13. Sandiego19

its okay thanks

14. jim_thompson5910

what do you mean SmoothMath?

15. SmoothMath

I don't think that good ol' Pythag can solve this problem.

16. jim_thompson5910

Since we have two right triangles, we can say b^2 + 29^2 = (21+a)^2 and a^2+20^2 = b^2 So we have a system of two equations with 2 unknowns. This means we can solve for a and b.

17. SmoothMath

Except that you're assuming this is a right angle, and that is not given: |dw:1337232422096:dw|

18. SmoothMath

Ah, but it can be proven.

19. jim_thompson5910

exactly

20. SmoothMath

Very good.

21. jim_thompson5910

it's not explicit, but the fact that the two triangles are similar allows us to use either method

22. SmoothMath

But a roundabout way to solve it indeed. Haha, funny that it's the first way you thought of.

23. jim_thompson5910

lol just been using it a lot more than the other method I guess