# isosceles trapezoid help

• Oct 19th 2009, 08:56 PM
cluap
isosceles trapezoid help
Old guy here who's forgotten everything and needs some help.

I'm trying to make an isosceles trapezoid with a base of 26 inches and an altitude of 16 inches. The sides come in with a 6 degree pitch (84 degree angles). What I'm trying to figure out is the length of the top section that parallels the base. I don't have a clue...

Thanks!
• Oct 20th 2009, 12:00 AM
earboth
Quote:

Originally Posted by cluap
Old guy here who's forgotten everything and needs some help.

I'm trying to make an isosceles trapezoid with a base of 26 inches and an altitude of 16 inches. The sides come in with a 6 degree pitch (84 degree angles). What I'm trying to figure out is the length of the top section that parallels the base. I don't have a clue...

Thanks!

1. Draw a rough sketch. (see attachment)

2. $\displaystyle t = 26- 2x$

3. Use the tan-function in the small right triangles:

$\displaystyle \tan(84^\circ)=\dfrac{16}x~\implies~x=\dfrac{16}{\ tan(84^\circ)} \approx 1.681667764...$

4. Therefore $\displaystyle \boxed{t \approx 22.63666447...}$
• Oct 20th 2009, 05:49 AM
Soroban
Hello, cluap!

This requires some Trigonometry.
I hope you're prepared.

Quote:

I'm trying to make an isosceles trapezoid with a base of 26 inches and an altitude of 16 inches.
The sides come in with a 6° (84° ngles).
What I'm trying to figure out is the length of the top section that parallels the base.

Code:

              B    x    C               * - - - - - *             /|          |\             / |          | \           /6°|          |  \           /  |16        |  \         /    |          |    \         /    |          |    \       / 84°  |          |      \     A * - - - * - - - - - * - - - * D           a  E    x    F  a       : - - - - -  26 - - - - - - :

We have isosceles trapezoid $\displaystyle ABCD.$
The base is: .$\displaystyle AD = 26.$
The height is: .$\displaystyle BE = 16$

Let: .$\displaystyle x \:=\:BC \:=\:EF$
Let: .$\displaystyle a \:=\:AE \:=\:FD$

Then: .$\displaystyle a + x + a \:=\:26 \quad\Rightarrow\quad x \:=\:26 - 2a$
. . Hence: .$\displaystyle BC \:=\:x \:=\:26 - 2a$ .[1]

In right triangle $\displaystyle BEA\!:\;\;\tan6^o \:=\:\frac{a}{16} \quad\Rightarrow\quad a \:=\:16\tan6^o \:\approx\:1.68$

Substitute into [1]: .$\displaystyle BC \:=\:26-2(1.68) \;=\;22.64\text{ inches}$

• Nov 2nd 2009, 05:10 PM
cluap
Guys - I'm sorry... I forgot to save the link, and I couldn't find this place again! Thanks for the help - you answered my questions in a way I could understand! Thanks for your help.

Take care, Paul