Find the resultant magnitude and bearing rounded to the tenth place for two tugboats towing a ship.

Question

Tugboat A: Pulls at a bearing of N 32 degrees W with a force of 4600 pounds.

Tugboat B: Pulls at a bearing of N 41 degrees E with a force of 6200 pounds.

Answer 1

N32E 4600

N41E 6200

this is worked with N32E instead of N32W

do the same basic method but get a very different answer with West instead of East

difference in angles = 41-32 = 9 degrees

SAS is a triangle

you know 2 sides and the angle between them

also construct a parallelogram

with 2 sides = 4600 and the other 2 sides = 6200

find the diagonal from the one 9 degree angle to the other 9 degree angle = resultant force

if the angle were zero, then the resultant force would be 10,800 lbs

but with 9 degrees, it is < 10,800 lbs

use law of sines or cosines to find the diagonal length

the other two angles of the parallelogram are (360-18)/2 =342/2=171 degrees

use the law of cosines to find the diagonal opposite 171 degrees

d^2 = 4600^2 + 6200^2 - 2(4600)(6200)Cos171 = the diagonal squared

d^2 =21,160,000+ 38,440,000 +56,337,742.95

d^2 = 59,600,000 +56,337,742.95

d^2= 115,937,742.95

d = sqr115,937,742.95

d =10,767.4 lbs.

bearing is about 37