Algebra and Trigonometry 10th Edition

$\sqrt {125+100 \cos \theta}$
We have: $F_1=10 \cos \theta$ and $F_2=5 \cos \theta+5 \sin \theta$ Now, $||F_1+F_2|| =\sqrt {(10 \cos \theta)^2+(5 \cos \theta+5 \sin \theta)^2}$ or, $=\sqrt {100 +100 \cos \theta+ 25 (\sin^2 \theta+\cos^2 \theta)}$ or, $=\sqrt {125+100 \cos \theta}$