# Finding the length of segment

• Mar 19th 2010, 11:18 PM
harold
Finding the length of segment
This one has been eating at me for a long time and I just can't figure it out:

In the figure below, ACDF is a parallelogram. Segment AE is perpendicular to line CD, and segment DB is perpendicular to line AC. The length of DB is 6 meters, segment FA is 9 meters and segment AC is 15 meters. How many meters long is segment AE?

How do I show/prove that it's 10 meters?
• Mar 19th 2010, 11:40 PM
earboth
Quote:

Originally Posted by harold
This one has been eating at me for a long time and I just can't figure it out:

In the figure below, ACDF is a parallelogram. Segment AE is perpendicular to line CD, and segment DB is perpendicular to line AC. The length of DB is 6 meters, segment FA is 9 meters and segment AC is 15 meters. How many meters long is segment AE?

How do I show/prove that it's 10 meters?

1. Calculate the sinus of the angle at C in the right triangle BCD:

$\sin(C)=\frac69$

2. Calculate the sinus of the angle at C in the right triangle ACE:

$\sin(C)=\frac69=\frac{\overline{AE}}{AC}$

3. Plug in all values you know: AC = 15, sin(C) to calculate

$|\overline{AE}| = \frac69 \cdot 15 = 10$
• Mar 20th 2010, 12:20 AM
harold
Thanks so much earboth--it was driving me crazy!!
• Mar 20th 2010, 03:31 PM
Recipe
Alternatively, you could recognize the similar triangles, so therefore

(9/15) = (6/x), thus x=10