Answer:
[tex]AB=20\sin 80^{\circ}\approx 19.7\ in\\ \\AC=20\sin 65^{\circ}\approx 18.1\ in\\ \\BC=20\sin 35^{\circ}\approx 11.5\ in[/tex]
Step-by-step explanation:
In triangle ABC, OA = OB = OC = 10 in. These segments are radii of sircumscribed circle. So, R = 10 in.
The sum of all interio angles is 180°, so
m∠C=180°-35°-65°=80°
Use the sine theorem,
[tex]\dfrac{AB}{\sin C}=\dfrac{AC}{\sin B}=\dfrac{BC}{\sin A}=2R[/tex]
Thus,
[tex]\dfrac{AB}{\sin 80^{\circ}}=\dfrac{AC}{\sin 65^{\circ}}=\dfrac{BC}{\sin 35^{\circ}}=20[/tex]
Therefore,
[tex]AB=20\sin 80^{\circ}\approx 19.7\ in\\ \\AC=20\sin 65^{\circ}\approx 18.1\ in\\ \\BC=20\sin 35^{\circ}\approx 11.5\ in[/tex]
