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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.

Respuesta :

jcherry99

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

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