(vector)Two tugs are towing a small ship. The tugs pull with forces of 600 N and 800 N respectively and there is an angle of 45 degrees between the two ropes. What is the magnitude and direction of the resultant force provided by the two tugs?

566.73 N and 78.7°

Explanation:

I've attached a diagram to show the forces and angle as indicated in the question.

From the free body diagram, we can see that the resultant force is labeled as C.

Using law of cosine, we can find C.

Thus:

C² = a² + b² - 2(ab)cos θ

C = √(a² + b² - 2(ab)cos θ)

C = √(600² + 800² - 2(600 × 800)(cos 45))

C = √(360000 + 640000 - (960000 × 0.7071))

C = 566.73 N

Direction will be gotten by using sine rule:

800/sin b = 566.73/sin 44

sin b = (800sin 44)/566.73

sin b = 0.9806

b = sin^(-1) 0.9806

b = 78.7°