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In right triangle ABC with the right angle at vertex A, altitude AE is drawn from vertex A to hypotenuse BC, AE = 21, and CE = 20. Find the length of BC. Round your answer to the nearest hundredth.

 Feb 10, 2020
 #1
avatar+1148 
0

Answer: 42.05 (units)

 

Explanation:

If AE is perpendicular to BC and CE = 20 with AE = 21, then AC = 29 by Pythagorean Theorem. 

Now, call AB x and BE y.

\(21^2+y^2=x^2\)

\(29^2+x^2=(y+20)^2\)

by Pythag.

 

Simplifying things...

\(x^2-y^2=441\)

\(x^2-y^2=40y-441\)

So \(441=40y-441, y=22.05\).

To find the lengh of BC, it's just BE+EC, or 22.05+20 = 42.05 un.

 

You are very welcome!

:P

 Feb 10, 2020
 #2
avatar+111389 
+1

Thanks, CoolStuffYT.....!!!!

 

Here's one more way  :

 

Note that  triangles  CAE  and CBA are similar

 

And using CoolSuffYT's   answer that  AC  =29   we have that

 

So

 

AC / EC  =  BC  / AC

 

29 / 20  =  BC  /  29

 

29^2 / 20  =  BC

 

841 / 20   = BC

 

42.05  =  BC

 

 

cool cool cool

 Feb 10, 2020
 #3
avatar+794 
+1

In right triangle ABC with the right angle at vertex A, altitude AE is drawn from vertex A to hypotenuse BC, AE = 21, and CE = 20. Find the length of BC. Round your answer to the nearest hundredth.

 

Triangles  ABC, ACE and ABE  are similar.

AE = 21

CE = 20

Angle ACB = ?              tan(ACB) = AE / CE        ∠ ACB = 46.397°

BE = tan(BAE) * AE           BE = 22.05

BC = CE + BE           BC = 42.05  indecision

 Feb 10, 2020

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