Jan 14, 2018

$\text{Details are shown below.}$

#### Explanation:

• The horizontal component of vector A is drawn in blue.

${A}_{x} = A . \cos \theta$

$- 20 = A . \cos \left(130\right)$

$\cos \left(130\right) = - \cos \left(50\right) = - 0.64278761$

$- 20 = A . \left(- 0.64278761\right)$

$A = \frac{- 20}{- 0.64278761}$

$A = 31.11 \text{ units}$

• The vector A is drawn in red.

• The vertical component of vector A is drawn in green.

$\cos \left(40\right) = \sin \left(50\right) = 0.76604444$

${A}_{y} = A . \cos \left(40\right) = 31.11 \cdot 0.76604444$

${A}_{y} = 31.11 \cdot 0.76604444$

${A}_{y} = 23.83 \text{ units}$