Question

Can someone solve this?

Answer 1

Answer:

Considering the Law of Cosines:

$c^2=a^2+b^2-2ab*cosC$

$a=14mi; b=24mi; c=CA; C=91degrees$

$\cos \left(91^{\circ \:}\right)=-0.01745\dots$

$c^2=14^2+24^2-2(14)(24)*\cos \left(91^{\circ \:}\right)\\c^2=196+576-672*\cos \left(91^{\circ \:}\right)\\c^2=772-672*\cos \left(91^{\circ \:}\right)\\c^2=772-672*(-0.01745)\\c^2=772+11.7264\\c=\sqrt{772+11.7264} \\c=\sqrt{783.7264}\\c=27.99mi$