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