Answer:
∠C = 70°
a = 32.66mm
b = 44.08mm
Step-by-step explanation:
Given:
∠A = 43°
∠B = 67°
c = 45mm
Solution:
•First, we need to find ∠C. Since the sum of all the three angles of a triangle is 180°,
∠A+∠B+∠C = 180°
∠C = 180°-∠A-∠B
∠C = 180°-43°-67°
∠C = 70°
•Second, we will use the formula above to find either a or b. This time, I will find the value of a first.
a/(sin A) = c/(sin C)
a(sin C) = c(sin A) — Cross multiply the two fractions
a = c(sin A)/(sin C) — Divide both sides by sin C
a = 45(sin 43)/(sin 70) — Use scientific calculator
a = 32.66mm
•Third, we will find the value of b.
b/(sin B) = c/(sin C)
b(sin C) = c(sin B) — Cross multiply the two fractions
b = c(sin B)/(sin C) — Divide both sides by sin C
b = 45(sin 67)/(sin 70) — Use scientific calculator
b = 44.08mm
