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.

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 CDThen 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^2EC = 20FC = ?EF= 24   This the Hypotenuse.10^2 + FC^2 = 24^2100 + FC^2 = 576                 Subtract 100 from both sides.FC^2 = 576 - 100                  Combine the right FC^2 = 476sqrt(FC^2) = sqrt(476)FC = 21.817

Step Two

Find CD. Do this by finding the area two ways. (Key Step)Area = hypotenuse * altitude / 2Area = EC * CF / 2EC = 10CF = 21.817hypotenuse = 24altitude = y24*y / 2 = 10 * 21.817 /212 y = 218.17/212y = 109.085y = 109.085/12y = 9.0904

Step Three

Find EDED^2 = 10^2 - y^2ED^2 = 100 - 9.0904^2ED^2 = 100 - 82.6357ED^2 = 17.36sqrt(ED^2) = sqrt(17.36)ED = 4.1671ED = 4.2

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