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 AB 14cm long. And AC 8cm long what will be the approximate angle of measure B

Answer 1

To find the approximate measure of angle B in triangle ABC, where AB is the diameter of the circle and AC is given, we can apply the properties of circles and the triangle itself.

Since AB is the diameter of the circle, angle C is a right angle (90 degrees) according to the inscribed angle theorem.

Given:
- AB (diameter) = 14 cm
- AC = 8 cm

We can use the Pythagorean theorem to find the length of BC. In right triangle ABC, where:
- \( AB^2 = AC^2 + BC^2 \)

Substituting the known values:
\[
14^2 = 8^2 + BC^2
\]
\[
196 = 64 + BC^2
\]
\[
BC^2 = 196 - 64
\]
\[
BC^2 = 132
\]
\[
BC = \sqrt{132} \approx 11.49 \text{ cm}
\]

Now we can find angle B using the sine function:
\[
\sin(B) = \frac{AC}{AB} = \frac{8}{14} = \frac{4}{7}
\]

To find angle B, we take the inverse sine (arcsin):
\[
B = \arcsin\left(\frac{4}{7}\right)
\]

Using a calculator, we find:
\[
B \approx 0.588 \text{ radians} \approx 33.69^\circ
\]

Thus, the approximate measure of angle B is **33.7 degrees**.