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.

Guest Feb 10, 2020

#1**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

CoolStuffYT Feb 10, 2020

#2**+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

CPhill Feb 10, 2020

#3**+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 _{}**

Dragan Feb 10, 2020