Answer
$27~sin(\omega t +8.5^{\circ})$
Work Step by Step
$\sum~E_h = 10~cos~0^{\circ}+ 15~cos~30^{\circ}+5.0~cos~(-45^{\circ}) = 26.526$
$\sum~E_v = 10~sin~0^{\circ}+ 15~sin~30^{\circ}+5.0~sin~(-45^{\circ}) = 3.964$
We can find the magnitude:
$E = \sqrt{(26.526)^2+(3.964)^2} = 27$
We can find the angle:
$\beta = tan^{-1}~(\frac{3.964}{26.526}) = 8.5^{\circ}$
The sum is: $~~27~sin(\omega t +8.5^{\circ})$
