# Roof Structure Question find lengths

• Dec 3rd 2006, 05:33 AM
zak_killcity14@hotmail.co
Roof Structure Question find lengths
http://i111.photobucket.com/albums/n...fstructure.gif
Find the rise of BD? :confused: :(
• Dec 3rd 2006, 05:59 AM
ThePerfectHacker
I give you a hint.

The area of Triangle ABD = area ABC +area BCD

Now, call $\displaystyle BD=h$, the height.

Then you can find,
$\displaystyle CD=\sqrt{4700^2-h^2}$

Thus,
area ABD=$\displaystyle (1/2)h(3300 +\sqrt{4700^2-h^2})$

area ABC can be computed by Heron's Formula

area BCD=$\displaystyle (1/2)h\sqrt{4700^2-h^2}$

You have an equation to solve for!
• Dec 3rd 2006, 06:03 AM
Soroban
Hello, Zak!

In $\displaystyle \Delta ABC$, use the Law of Cosines to find $\displaystyle \angle ACB.$

$\displaystyle \cos(\angle ACB)\:=\:\frac{3300^2 + 4700^2 - 7000^2}{2(3300)(4700)}\:=\:-0.516441006$

Hence: .$\displaystyle \angle ACB \:\approx\:121.1^o$

Then: .$\displaystyle \angle BCD\:=\:180^o - 121.1^o \:=\:58.9^o$

In right triangle $\displaystyle BDC\!:\;\;\sin 58.9^o \:=\:\frac{BD}{4700}$

Therefore: .$\displaystyle BD \:=\:4700\sin58.9^o \:=\:4024.717024 \:\approx\:4025$

• Dec 3rd 2006, 05:58 PM
Soroban
Hello, Zak!

An alternate approach . . .

In $\displaystyle \Delta ABC$, use the Law of Cosines to find angle $\displaystyle A.$

$\displaystyle \cos A\:=\:\frac{7000^2 + 3300^2 - 4700^2}{2(7000)(3300)} \:=\:0.8181818181$

. . Hence: .$\displaystyle A \:\approx\:35.1^o$

In right triangle $\displaystyle BDA\!:\;\sin 35.1^o \:= \:\frac{BD}{7000}\quad\Rightarrow\quad BD \:=\:7000\sin35.1^o \:=\:4025.036764$

. . Therefore: .$\displaystyle BD \:\approx\:4025$