Answer:
[tex] b = 5.5 [/tex]
[tex] c = 11.2 [/tex]
Step-by-step explanation:
Given:
A = 96°
B = 25°
C = 59°
a = 13
Required:
b and c
SOLUTION:
Use Sine Rule to find the measure of a and b, respectively.
✍️Thus, to find b, use,
[tex] \frac{a}{sin(A)} = \frac{b}{sin(B)} [/tex]
Plug in the values
[tex] \frac{13}{sin(96)} = \frac{b}{sin(25)} [/tex]
Multiply both sides by sin(25)
[tex] \frac{13}{sin(96)} \times sin(25) = \frac{b}{sin(25)} \times sin(25) [/tex]
[tex] \frac{13 \times sin(25)}{sin(96)} = b [/tex]
[tex] b = 5.5 [/tex] (nearest tenth)
✍️To find c, use,
[tex] \frac{a}{sin(A)} = \frac{c}{sin(C)} [/tex]
Plug in the values
[tex] \frac{13}{sin(96)} = \frac{c}{sin(59)} [/tex]
Multiply both sides by sin(59)
[tex] \frac{13}{sin(96)} \times sin(59) = \frac{c}{sin(25)} \times sin(59) [/tex]
[tex] \frac{13 \times sin(59)}{sin(96)} = c [/tex]
[tex] c = 11.2 [/tex] (nearest tenth)
