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.

#### Solution:

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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.

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.

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.

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

#### Final Answer:

See more examples similar to this question like finding the lengths of wires using the same method.