# Determine the length of member AB of the truss

Determine the length of member AB of the truss by first establishing a Cartesian position vector from A to B and then determining its magnitude. Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

#### Solution:

Let’s first figure out where point A and B is with respect to the origin (0i+0j+0k). Let’s write the location of point A in Cartesian vector notation.

$A:(0.8i+1.2j)$ m

To find point B, we will have to use trigonometry. We need to figure out the length of $a$ so that we can figure out the total x-axis length of point B. To do so, we can write an equation using the tangent function.

$\tan40^0\,=\,\dfrac{1.5}{a}$

$a\,=\,1.79$ m

Therefore, the total x-length of point B is 0.8 + 0.3 + 1.79 = 2.89 m.

Let us now write point B in Cartesian vector notation.

$B:(2.89i+1.5j)$ m

We can now find the position vector $r_{AB}$ by subtracting the corresponding coordinates of A from B.

$r_{AB}\,=\,\left\{(2.89-0.8)i+(1.5-1.2)j\right\}$ m

$r_{AB}\,=\,\left\{(2.09)i+(0.3)j\right\}$

We can now figure out the length of member AB by finding the magnitude of $r_{AB}$.

magnitude of $r_{AB}\,=\,\sqrt{(2.09^2)+(0.3)^2}\,=\,2.11$ m