In a circle, if a triangle is inscribed such that one of its sides is the diameter of the circle, then the angle opposite to that side is a right angle (90°). This is known as the Inscribed Angle Theorem.
In Regina's triangle ABC, since AB is the diameter of the circle, angle C (the inscribed angle) must be 90°.
To find angle B, we can use the relationship between the sides and angles in triangle ABC. We know that:
- The length of AB (the hypotenuse) is 14 cm.
- The length of AC is 8 cm.
Using the Pythagorean theorem in triangle ABC, we can find BC: \[ AB^2 = AC^2 + BC^2 \] \[ 14^2 = 8^2 + BC^2 \] \[ 196 = 64 + BC^2 \] \[ BC^2 = 196 - 64 = 132 \] \[ BC = \sqrt{132} \approx 11.49 \text{ cm} \]
Now we can find angle B using the sine function: \[ \sin(B) = \frac{AC}{AB} = \frac{8}{14} = \frac{4}{7} \approx 0.571 \]
Now, find angle B: \[ B \approx \sin^{-1}(0.571) \approx 35° \]
Thus, the approximate angle measure of B is 35°.
The correct response is: 35°