Question

Line segment CD is the altitude drawn to hypotenuse EF in right triangle ECF. If EC = 10 and EF = 24, then, to the nearest tenth, find ED.

Answer 1

4.2 = ED

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