Determine the values of angle a and theta so that the forces shown in figure below equilibrium Problem No. 1Determine the values of angles a and e s0 that the forcesshown in figure below will be in equilibrium...20 lb401630 1b

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Determine the values of angles a and e s0 that the forces shown in figure below will be in equilibrium... 201b 4016

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Determine the values of angle a and theta so that the forces shown in figure below equilibrium

Problem No. 1
Determine the values of angles a and e s0 that the forces
shown in figure below will be in equilibrium...
20 lb
4016
30 1b

Expert Solution

Step 1

Cosine law represents the relation between the length of sides of triangle with cosines of its angle. If ABC is the triangle then cosine law gives the equation,

$a^{2} = b^{2} + c^{2} - 2 bc \cos (α)$

where a, b and c are sides of a triangle and $α$ is angle between side b and c.

Here $a = 30 lb$ , $b = 20 lb$ and $c = 40 lb$ and the angle between b and c is $α$ .

Use cosine law,

$\begin{array}{rcl} {(30 lb)}^{2} & = & {(20 lb)}^{2} + {(40 lb)}^{2} - 2 \times 20 lb \times 40 lb \times cosα \\ 900 & = & 400 + 1600 - 1600 \times cosα \\ 1100 & = & 1600 \times cosα \\ cosα & = & \frac{1100}{1600} \\ α & = & \cos^{- 1} (0.6875) \\ α & = & 46.6 ° \end{array}$