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