Answer:
c = 13.1
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ ABC
# ∠A is opposite to side a
# ∠B is opposite to side b
# ∠C is opposite to side c
- The sine rule is:
# [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
* Lets solve the problem
- In Δ ABC
∵ m∠A = 57°
∵ m∠B = 37°
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ m∠A + m∠B + m∠C = 180°
∴ 57° + 37° + m∠C = 180°
∴ 94° + m∠C = 180° ⇒ subtract 94° from both sides
∴ m∠C = 86°
- Lets use the sine rule to find c
∵ a = 11 and m∠A = 57°
∵ m∠C = 86°
∵ [tex]\frac{sin(57)}{11}=\frac{sin(86)}{c}[/tex]
- By using cross multiplication
∴ c sin(57) = 11 sin(86) ⇒ divide both sides by sin(57)
∴ [tex]c=\frac{11(sin86)}{sin57}=13.1[/tex]
* c = 13.1
