Question

In triangle ABC, ZA = 55°, m2 B = 30°, and a = 8. Which equation should you solve to find b?

A. sin55°/sin30° = 5/8
B. cos(55°)/cos(30°) = 5/8
C. ( b² = 8² - 2(8) × b × cos(30°) )
D. sin(55°)sin(30°) = 6

Answer 1

To find side b in triangle ABC with given angles and side a, use the Law of Sines. Formulate the equation as sin(55°) / sin(30°) = 8 / b, and solve for b.

Step-by-step explanation:

In triangle ABC, with ZA = 55°, m2 B = 30°, and side a measuring 8, to find side b we should use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. This can be written as:

a / sin A = b / sin B = c / sin C

Given this, we can set up the equation:

sin(55°) / sin(30°) = 8 / b

Which can be rearranged to solve for b:

b = 8 · sin(30°) / sin(55°)

Hence, the appropriate equation to find b is option A:

sin(55°) / sin(30°) = 8 / b