Answer:
7. A ≈ 60.1°
8. B ≈ 34.0°
9. C ≈ 33.1°
Step-by-step explanation:
7.
The Law of Sines states that for a triangle with lengths a, b, and c and angles A, B, and C: [tex]\frac{a}{sinA}= \frac{b}{sinB} =\frac{c}{sinC}[/tex].
Here, we can say that a = 7, b = 8, and B = 82, and we want to find A. Plug these values in:
[tex]\frac{a}{sinA} =\frac{b}{sinB}[/tex]
[tex]\frac{7}{sinA} =\frac{8}{sin(82)}[/tex]
Solve for A:
A ≈ 60.1°
8.
Again, use the Law of Sines as above:
[tex]\frac{b}{sinB} =\frac{c}{sinC}[/tex]
[tex]\frac{14}{sin(37)} =\frac{13}{sinB}[/tex]
Solve for B:
B ≈ 34.0°
9.
Use the Law of Sines as above:
[tex]\frac{a}{sinA} =\frac{c}{sinC}[/tex]
[tex]\frac{17}{sin(68)} =\frac{10}{sinC}[/tex]
Solve for C:
C ≈ 33.1°
