Answer :
Answer:
4.2 = ED
Step-by-step explanation:
- C is the Right Angle.
- You will do yourself a great favor by drawing your own diagram.
- The easiest way to do this is to find CF first. Use the Pythagorean Theorem.
- The next step is to find the area of the triangles using EC * CF which you just found. Equate that to the hypotenuse * altitude(CD) to find CD
- Then use Pythagoras again to ED.
Step One
Find FC. That is the only side of the right triangle that you don't know the value of.
- EC^2 + FC^2 = EF^2
- EC = 20
- FC = ?
- EF= 24 This the Hypotenuse.
- 10^2 + FC^2 = 24^2
- 100 + FC^2 = 576 Subtract 100 from both sides.
- FC^2 = 576 - 100 Combine the right
- FC^2 = 476
- sqrt(FC^2) = sqrt(476)
- FC = 21.817
Step Two
- Find CD. Do this by finding the area two ways. (Key Step)
- Area = hypotenuse * altitude / 2
- Area = EC * CF / 2
- EC = 10
- CF = 21.817
- hypotenuse = 24
- altitude = y
- 24*y / 2 = 10 * 21.817 /2
- 12 y = 218.17/2
- 12y = 109.085
- y = 109.085/12
- y = 9.0904
Step Three
- Find ED
- ED^2 = 10^2 - y^2
- ED^2 = 100 - 9.0904^2
- ED^2 = 100 - 82.6357
- ED^2 = 17.36
- sqrt(ED^2) = sqrt(17.36)
- ED = 4.1671
- ED = 4.2