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

- anonymous

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- anonymous

##### 1 Attachment

- cwrw238

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- 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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## More answers

- anonymous

awesome thanks

- anonymous

So the length of the altitude would be 147?

- cwrw238

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

- anonymous

hmmm same here

- anonymous

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

- cwrw238

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

- cwrw238

*big triangle ABC

- anonymous

ok

- 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

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

- cwrw238

no 21 and 7 = BC

- cwrw238

the way the triangles are its hard to explain
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- anonymous

That is hard T_T

- 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

right that means that x= 4 right?

- cwrw238

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

- anonymous

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

- cwrw238

you need the height right?
thats AD

- anonymous

I need the height of the altitude drawn to the hypotenuse

- cwrw238

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

- anonymous

ok

- 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

oh ok so how do I solve for AC?

- 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

right

- cwrw238

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- 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

ok

- 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

ah ok

- cwrw238

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

- anonymous

hmmm i see, ok

- 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

O.o ok

- cwrw238

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

- anonymous

Ah ok i see

- cwrw238

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

- anonymous

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