230 Distance from truss member to truss joint

Let
d = length of member BD
d_x = 12 ft
d_y = 16 - 12 = 4 ft

$d = \sqrt{12^2 + 4^2}$

$d = 4\sqrt{10}$
 

 

Moment about point E
$M_E = 16d_x = 16(12)$

$M_E = 192 \, \text{ ft}^2$
 

$M_E = d_E \times d$

$192 = d_E(4\sqrt{10})$

$d_E = 15.18 \, \text{ ft}$           answer
 

Moment about point G
$M_G = 16d_x + 12d_y = 16(12) + 12(4)$

$M_G = 240 \, \text{ ft}^2$
 

$M_G = d_G \times d$

$240 = d_G(4\sqrt{10})$

$d_G = 18.974 \, \text{ ft}$           answer
 

Checking (by Geometry):
 

 

$\dfrac{x + 12}{12} = \dfrac{3}{1}$

$x = 24 \, \text{ ft}$
 

$\dfrac{d_E}{x + 24} = \dfrac{1}{\sqrt{10}}$

$d_E = \dfrac{24 + 24}{\sqrt{10}}$

$d_E = 15.18 \, \text{ ft}$           (okay!)
 

$\dfrac{d_G}{x + 36} = \dfrac{1}{\sqrt{10}}$

$d_G = \dfrac{24 + 36}{\sqrt{10}}$

$d_G = 18.974 \, \text{ ft}$           (okay!)