Question

Regina draws a triangle inside a circle; she labels the vertices ABC
, with the diameter as AB
and the inscribed angle as C
. She draws the length of AB
14 cm long, and AC
8 cm long. Using what you know about inscribed angles, what will be the approximate angle measure of B
?(1 point)

90°

35°

55°

70°

Answer 1

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

sin(B) = AC/AB = 8/14 = 4/7 ≈ 0.5714, so B ≈ arcsin(0.5714) ≈ 35°.

Answer: 35°.