Answer
$θ\approx40.25º$
Work Step by Step
In this exercise, one must first find the opposite side of the 75º using the law of cosine and then use the law of sine to find θ. So, the opposite side will be:
$\sqrt{7^2+5^2-2(7)(5)\cdot cos(75º)}=$
$\sqrt{49+25-70\cdot 0.26}=$
$\sqrt{74-18.12}=$
$\sqrt{55.88}\approx 7.48$
Now, θ can be found:
$\frac{sin(75º)}{7.48}=\frac{sin(θ)}{5}$
$θ=$sin$^{-1}(5\cdot \frac{sin(75º)}{7.48})$
$θ=$sin$^{-1}(5\cdot 0.13)\approx40.25º$
