perpendicular segment measure

**rcs** · December 22nd 2012, 06:23 AM

Let ABCD be a square with each side of length 2cm. Let E be the midpoint of AB. How long is the perpendicular segment C to DE?

can anyone help me on this please

**skeeter** · December 22nd 2012, 06:29 AM

make a sketch ... use the fact that the sides of similar triangles are proportional.

**rcs** · December 22nd 2012, 07:07 AM

is this correct 2* sqrt(5) / 5

**Soroban** · December 22nd 2012, 07:46 PM

JHello, rcs!

Your answer is close, but . . .

Let ABCD be a square with each side of length 2cm.
Let E be the midpoint of AB.
How long is the perpendicular segment from C to DE?

Code:

            1     E
    A o - - - - - o - - - - - o B
      |        θ /            |
      |         /             |
      |      F /              |
      |    _  o               |
      |   √5 /  *             |
    2 |     /     *           |
      |    /        *         |
      |   /           *       |
      |  /              *     |
      | /                 *   |
      |/ θ                  * |
    D o - - - - - - - - - - - o C
                  2

In right triangle $EAD$ , the hypotenuse is: $DE \,=\,\sqrt{1^2+2^2} \,=\,\sqrt{5}$

Right triangles $EAD$ and $DFC$ have angle $\theta$ .
. . Hence: . $\Delta EAD \sim \Delta DFC$

$\begin{array}{cccccccc}\text{In }\Delta DFC:& \sin\theta &=& \dfrac{CF}{2} \\ \\[-3mm] \text{In }\Delta EAD: & \sin\theta &=& \dfrac{2}{\sqrt{5}} \end{array}$

Therefore: . $\frac{CF}{2} \:=\:\frac{2}{\sqrt{5}} \quad\Rightarrow\quad CF \:=\:\frac{4}{\sqrt{5}} \;=\;\frac{4\sqrt{5}}{5}$

Thread: perpendicular segment measure

LinkBack

Thread Tools

Display

perpendicular segment measure

Re: perpendicular segment measure

Re: perpendicular segment measure

Re: perpendicular segment measure

Similar Math Help Forum Discussions

measure theory-Lebesgue measure

Statistical Probability measure and probability measure difference?

Showing that a specific outer measure is a measure

A finite additive measure that is continuous from below is a measure

Finite additive measure is a measure if it is continuous from below

Search Tags