Given C =128°, a=10.01, and c=18, use the Law of Sines to solve the triangle (if
possible) for the value of b. If two solutions exist, find both. Round answer to two
decimal places.
A) b = 3.46
B) b=0.65 and 2.80
C) b=10.01
D) b=11.96 and 4.10
E) not possible

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west