Using the law of sines, we found that m∠B ≈ 43.7° and c ≈ 3.98 for the given triangle with m∠A=80∘, a=6.17, and b=4.22.
a. To find the value of m∠B, we can use the law of sines, which states that a/sinA = b/sinB.
Rearranging this equation to solve for sinB, we get sinB = (b/a) * sinA.
Plugging in the given values, we get sinB = (4.22/6.17) * sin(80°) ≈ 0.686.
Taking the inverse sine of this value, we find that m∠B ≈ 43.7°.
b. To find the value of c, we can again use the law of sines.
Using the same equation as before, but solving for c instead, we get c = (a * sinB)/sinA.
Plugging in the known values, we get c = (6.17 * sin(43.7°))/sin(80°) ≈ 3.98.