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1. In ABC, A=45 degrees, B=75 degrees, and BC=12. What is the length of AB?

Hello Guest!

Sine law

\(sin (A):12=sin(C):\overline{AB}\\ \overline{AB}\cdot sin(A)=12\cdot sin(C)\\ C=180°-45°-75°\\ C=60° \)

\(\overline{AB}=\frac{12\cdot sin(C)}{sin(A)}=\frac{12\cdot sin(60°)}{sin(45°)}=\frac{12\cdot \frac{1}{2}\sqrt{3}}{\frac{1}{2}\sqrt{2}}\\ =12\sqrt{\frac{3}{2}} \)

\(\overline{AB}=6\cdot \sqrt{2}\cdot \sqrt{3}\)

\(\overline{AB}=14.697\)

  !