In triangle ABC, angle A measures 50 degrees, side AB measures 10 units, and side BC measures 12 units. Find the measure of angle B by using the Law of sine.

Given data

→ Angle A = 50°

→ Side AB (opposite A) = 10 units

→ Side BC (opposite B) = 12 units

Apply the Law of Sines:

The Law of Sines states: \$("sin"(A))/"a" = ("sin"("B"))/"b"\$ where A and B are angles and a and b are the sides opposite to those angles.

Cross multiply to solve for sin(B):

\$sin(B) = (12 \times sin(50°)) / 10\$

Find angle B using inverse sine:

\$B = sin^-1 ((12 \times sin(50°)) / 10)\$

First, calculate the value inside the sine function:

\$ ((12 \times sin(50°)) / 10)\$

\$((12 \times 0.766) / 10)\$(i.e., since sin(50) = 0.766)

\$9.192/10\$ = 0.9192

Using a calculator or table, you’ll find the angle whose sine is approximately 0.9192.

B = arcsin(0.9192)
B = 67.08°

Therefore, the measure of angle B is approximately equal to 67.08°.

This option represents a fixed angle measure. It doesn’t correspond to the calculated value of angle B, which is approximately 67.85°

40°

This option is also smaller than the given angle A (50 degrees), which contradicts the fact that angle B should be larger than angle A due to the longer side BC. Therefore, it’s not the correct answer

45°

This option is not correct. Although it’s closer to the calculated value of B than options A and B, it’s still smaller than the calculated value of approximately 67.85°

55°

This option represents a fixed angle measure. While it doesn’t match the calculated value of angle B exactly, it’s the closest option to the calculated value of approximately 67.85°

60°

Option

D

Can you summarize what you’ve understood in the above steps?