Answer
$\approx 28.66 N$; $\approx12.37 ^\circ$
Work Step by Step
Top vector $= (20 cos 45) i+(20 sin 45)j =10 \sqrt 2 i+10 \sqrt 2 j$
Bottom vector $= (16 cos 30) i+(-16 sin 30)j =8 \sqrt 3 i-8j$
Horizontal component : $10 \sqrt 2 i+8 \sqrt 3 i=(10 \sqrt 2 +8 \sqrt 3 )i$
Vertical component: $10 \sqrt 2 j-8j=(10 \sqrt 2 -8)j$
$\approx 28.66 N$; $\approx12.37 ^\circ$
Resultant force: $(10 \sqrt 2 +8 \sqrt 3 )i+(10 \sqrt 2 -8)j=\sqrt {(10 \sqrt 2 +8 \sqrt 3 )^2+(10 \sqrt 2 -8)^2}\approx 28.66 N$
$tan \theta =\dfrac{vertical}{horizontal}=\frac {(10 \sqrt 2 -8 )} {(10 \sqrt 2+\sqrt 3)}$
$\theta =arctan[\dfrac{vertical}{horizontal}=\frac {(10 \sqrt 2 -8 )} {(10 \sqrt 2+\sqrt 3)}]$
$ \theta \approx 12.37 ^\circ$
