Points A and B are separated by a lake To find the distance

Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point Con land such that ACB = 42 degree. He also measures CA as 5.6 miles and CB as 3.2 miles. Find the distance between A and B. () Two tugboats that are a = 120 ft apart pull a barge, as shown. If the length of one cable is b - ISO ft and the length of the other is c = 200 ft, find the angle formed by the two cables. (Round your answer to the nearest degree.)

Solution

We have to use cosine law here

AB²=CA²+CB²-2CA CB cos <ACB

AB²= 5.6²+3.2²-2(5.6)(3.2) cos 42

AB²= 41.6 - 35.84 cos 42

AB =3.9 miles

d. using cosine law

a²= b²+c²-2bc cos A

120²= 180²+200²-2(180)(200)cos A

72000 cos A= 58000

Cos A= 58/72

A=36 degree

Therefore the angle formed by the two cables is 36 degree