Question

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

70°
70°

55°
55°

90°
90°

35°

Answer 1

AB is a diameter, so ∠C = 90° (Thales' theorem). In right triangle ABC, sin ∠B = opposite/hypotenuse = AC/AB = 8/14 = 4/7 ≈ 0.5714.
∠B ≈ arcsin(0.5714) ≈ 35°.