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.
+1253 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
+128474 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
+1486 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 
