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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
 one year ago
 one year 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
 one year ago
 one year ago

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cwrw238Best ResponseYou've already chosen the best response.1
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
 one year ago

math_crasherBest ResponseYou've already chosen the best response.0
So the length of the altitude would be 147?
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
no  i'm a bit confused myself now  not sure if we got enough info to do this
 one year ago

math_crasherBest ResponseYou've already chosen the best response.0
I just multiplied 7 and 21 and figured it would be the geometric mean Xd
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
no don't work like that take gig triangle the side opposite the right angle = 28 long right?
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
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
 one year ago

math_crasherBest ResponseYou've already chosen the best response.0
Ah ok so you added 21 and 7 and that is equals to AC?
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
the way the triangles are its hard to explain dw:1346867633370:dw
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
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?
 one year ago

math_crasherBest ResponseYou've already chosen the best response.0
right that means that x= 4 right?
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
exactly 3/6 = 2/x so x = 4
 one year ago

math_crasherBest ResponseYou've already chosen the best response.0
But what am I trying to solve in the previous triangle?
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
you need the height right? thats AD
 one year ago

math_crasherBest ResponseYou've already chosen the best response.0
I need the height of the altitude drawn to the hypotenuse
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
yea  thas length of AD  BC is the hypotenuse of the big triangle ABC
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
but we have to find length of AC first because we only know the 2 values 7 and 21.  you'll see why later
 one year ago

math_crasherBest ResponseYou've already chosen the best response.0
oh ok so how do I solve for AC?
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
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?
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
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
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
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
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
so AC 7  =  28 AC cross multiply AC^2 = 7*28 = 196
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
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
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
yea  thats a tricky one  you get wingspaneyed figuring out how 2 triangles are related
 one year ago

cwrw238Best ResponseYou've already chosen the best response.1
i think i'll take a break  lol!!
 one year ago

math_crasherBest ResponseYou've already chosen the best response.0
dw:1346869580845:dw
 one year ago
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