Question

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)
Responses

90°
90°

35°
35°

55°
55°

70°

Answer 1

Since triangle ABC is inscribed in a circle with AB as the diameter, angle C is a right angle according to the inscribed angle theorem. This means that angle B is not directly calculated but can be found using the sides of the triangle.

Given:
- AB = 14 cm
- AC = 8 cm

Using the Pythagorean theorem, we can find the length of side BC. Let the length of BC be represented as \( c \).

According to the Pythagorean theorem:

\[
AC^2 + BC^2 = AB^2
\]

Substituting the values we have:

\[
8^2 + c^2 = 14^2
\]

This simplifies to:

\[
64 + c^2 = 196
\]

Subtracting 64 from both sides gives:

\[
c^2 = 196 - 64
\]
\[
c^2 = 132
\]
\[
c = \sqrt{132} \approx 11.49 \text{ cm}
\]

Now, we can use the sine rule or tangent to find angle B.

Using the sine function:

\[
\sin(B) = \frac{AC}{AB}
\]

Substituting the known lengths:

\[
\sin(B) = \frac{8}{14} = \frac{4}{7} \approx 0.5714
\]

Now, we calculate angle B:

\[
B \approx \arcsin(0.5714) \approx 35°
\]

Thus, the approximate angle measure of B is **35°**.