Answer:
b = 6.7cm
Step-by-step explanation:
The law of sines is:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex] OR [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]
Each section represents an angle (capital) and its opposite side (lowercase). When you use it, only use two sections at a time. You may have one missing piece of information when using it. Use the formula that puts the missing information in the numerator (top).
This problem:
We are given one set of information, 8cm and 55°. This can be "a" and "A" (not labelled).
We need angle B to find side b.
Since we are given two of the three angles in the triangle, and the sum of all interior angles of any triangle is 180°, we can find the missing angle.
∠B = 180° - (∠A + ∠C)
∠B = 180° - (55° + 82°)
∠B = 43°
Use the law of sines with sections "A" and "B", with the lowercase letters in the top.
[tex]\frac{a}{sinA} =\frac{b}{sinB}[/tex] Substitute known measurements
[tex]\frac{8cm}{sin(55)} =\frac{b}{sin(43)}[/tex] Rearrange to isolate "b"
[tex]b = \frac{8cm}{sin(55)}X{sin(43)}[/tex] Solve, degree mode on calculator
[tex]b = 6.660...cm[/tex] Exact answer
[tex]b = 6.7cm[/tex] Rounded to nearest tenth
Therefore side b is 6.7cm.
