anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
1 Attachment
cwrw238
  • cwrw238
|dw:1346866520983:dw|
cwrw238
  • 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

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anonymous
  • anonymous
awesome thanks
anonymous
  • anonymous
So the length of the altitude would be 147?
cwrw238
  • cwrw238
no - i'm a bit confused myself now - not sure if we got enough info to do this
anonymous
  • anonymous
hmmm same here
anonymous
  • anonymous
I just multiplied 7 and 21 and figured it would be the geometric mean Xd
cwrw238
  • cwrw238
no don't work like that take gig triangle the side opposite the right angle = 28 long right?
cwrw238
  • cwrw238
*big triangle ABC
anonymous
  • anonymous
ok
cwrw238
  • 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
anonymous
  • anonymous
Ah ok so you added 21 and 7 and that is equals to AC?
cwrw238
  • cwrw238
no 21 and 7 = BC
cwrw238
  • cwrw238
the way the triangles are its hard to explain |dw:1346867633370:dw|
anonymous
  • anonymous
That is hard T_T
cwrw238
  • 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?
anonymous
  • anonymous
right that means that x= 4 right?
cwrw238
  • cwrw238
exactly 3/6 = 2/x so x = 4
anonymous
  • anonymous
But what am I trying to solve in the previous triangle?
cwrw238
  • cwrw238
you need the height right? thats AD
anonymous
  • anonymous
I need the height of the altitude drawn to the hypotenuse
cwrw238
  • cwrw238
yea - thas length of AD - BC is the hypotenuse of the big triangle ABC
anonymous
  • anonymous
ok
cwrw238
  • 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
anonymous
  • anonymous
oh ok so how do I solve for AC?
cwrw238
  • 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?
anonymous
  • anonymous
right
cwrw238
  • cwrw238
|dw:1346868513347:dw|
cwrw238
  • 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
anonymous
  • anonymous
ok
cwrw238
  • 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
anonymous
  • anonymous
ah ok
cwrw238
  • cwrw238
so AC 7 -- = -- 28 AC cross multiply AC^2 = 7*28 = 196
anonymous
  • anonymous
hmmm i see, ok
cwrw238
  • 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
anonymous
  • anonymous
O.o ok
cwrw238
  • cwrw238
yea - thats a tricky one - you get wingspan-eyed figuring out how 2 triangles are related
anonymous
  • anonymous
Ah ok i see
cwrw238
  • cwrw238
-i think i'll take a break - lol!!
anonymous
  • anonymous
|dw:1346869580845:dw|

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