Question

Regina draws a triangle inside a circle; she labels the vertices $ABC$, with the diameter as $\overline{AB}$ and the inscribed angle as $C$. She draws the length of $\overline{AB}$ 14 cm long, and $\overline{AC}$ 8 cm long. Using what you know about inscribed angles, what will be the approximate angle measure of $B$?Responses35° 90°55°70°

Answer 1

Because AB is a diameter, angle C is a right angle (Thales' theorem). So AB = hypotenuse = 14 and AC = side opposite angle B = 8.

sin B = opposite/hypotenuse = 8/14 = 4/7, so B = arcsin(4/7) ≈ 34.85° ≈ 35°.

Answer: 35°.