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)
Based on the given information, we know that AC is a chord of the circle, AB is the diameter, and angle C is the inscribed angle.
By the inscribed angle theorem, we know that the angle formed by the inscribed angle is half of the central angle that creates the same arc. In this case, the central angle would be angle CAB.
Since AC is 8 cm long and AB is 14 cm long, the arc created by angle CAB is the arc ACB. Therefore, angle CAB is the central angle of arc ACB, and angle C is the inscribed angle that corresponds to the same arc.
To find the central angle, we can use the formula for the length of an arc: (arc length) = (angle measure / 360) * (2 * π * radius).
We know that arc ACB corresponds to a length of 8 cm (radius is half of AB, which is the diameter). The radius of the circle is therefore 7 cm.
So, (8) = (angle / 360) * (2 * π * 7).
Solving for angle gives us approximately 104.57 degrees for the measure of angle CAB. Therefore, the approximate angle measure of angle B is half of this, or approximately 52.29 degrees.