This is a Trigonometry question please solve by treating the

This is a Trigonometry question, please solve by treating the Boats as vectors, NOT FORCES.

Two tugboats are pulling on a large ship that has gone aground. One tug pulls with a force of 2500 pounds in a compass direction of 55 degree. The second tug pulls with a force of 2000 pounds in a compass direction of 95 degree. Find the magnitude and the compass direction of the resultant force. This is a Trigonometry question, please solve by treating the Boats as vectors, NOT FORCES.

Solution

resultant force of two vectors a and b is

R²= a²+b²+2ab Cosine of(angle between vectors)

R²=2500 ² + 2000 ² + 2 X 2500X2000X Cos(95-55)

R²=6250000+4000000+2X10000000X Cos(40)

R=sqroot(10250000+15320888.86)=sqroot(25570888.86)=5056 Pounds is the mangnitude. and angle=17.7