## math_crasher 3 years ago Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale. Pls explain to me how to do this. Figure is below

1. math_crasher

2. cwrw238

|dw:1346866520983:dw|

3. cwrw238

the 2 triangles ACD and ABC are similar (same shape - corresponding angles are equal) the property of similar triangles is that corresponding sides are in the same ratio

4. math_crasher

awesome thanks

5. math_crasher

So the length of the altitude would be 147?

6. cwrw238

no - i'm a bit confused myself now - not sure if we got enough info to do this

7. math_crasher

hmmm same here

8. math_crasher

I just multiplied 7 and 21 and figured it would be the geometric mean Xd

9. cwrw238

no don't work like that take gig triangle the side opposite the right angle = 28 long right?

10. cwrw238

*big triangle ABC

11. math_crasher

ok

12. cwrw238

now look at small on ABD the side opposite right angle is AC AC is side corresponding to the one 28 long so the ratio is AC -- 28

13. math_crasher

Ah ok so you added 21 and 7 and that is equals to AC?

14. cwrw238

no 21 and 7 = BC

15. cwrw238

the way the triangles are its hard to explain |dw:1346867633370:dw|

16. math_crasher

That is hard T_T

17. cwrw238

the 2 triangles are similar - the sides are different in length but the angles are same 3 in small trianglee corresponds to 6 in big one and 2 in small triangle corresponds to x in gig one righr?

18. math_crasher

right that means that x= 4 right?

19. cwrw238

exactly 3/6 = 2/x so x = 4

20. math_crasher

But what am I trying to solve in the previous triangle?

21. cwrw238

you need the height right? thats AD

22. math_crasher

I need the height of the altitude drawn to the hypotenuse

23. cwrw238

yea - thas length of AD - BC is the hypotenuse of the big triangle ABC

24. math_crasher

ok

25. cwrw238

but we have to find length of AC first because we only know the 2 values 7 and 21. - you'll see why later

26. math_crasher

oh ok so how do I solve for AC?

27. cwrw238

by using similar triangle property we already got AC / 28 now look at the 2 triangles ABC and ACD the side CD (=7) in the small triangle is opposite the angle CAD right?

28. math_crasher

right

29. cwrw238

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30. cwrw238

the 2 angles marked x are equal and the side opposite angle B in big triangle = AC so this means that the side correspond to CD in small triangle is corresponding to AC in big triangle

31. math_crasher

ok

32. cwrw238

not easy to see this because the way the triangles are related ratio of these sides in small : big = 7 /AC and this equals AC / 28 which we got already

33. math_crasher

ah ok

34. cwrw238

so AC 7 -- = -- 28 AC cross multiply AC^2 = 7*28 = 196

35. math_crasher

hmmm i see, ok

36. cwrw238

so - the last step! apply pythagoras theorem to triangle ADC: AC^2 = 7^2 + AD^2 196 = 49 + ad^2 AD^2 = 196 - 49 = 147 AD = square root of 147

37. math_crasher

O.o ok

38. cwrw238

yea - thats a tricky one - you get wingspan-eyed figuring out how 2 triangles are related

39. math_crasher

Ah ok i see

40. cwrw238

-i think i'll take a break - lol!!

41. math_crasher

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