Ship A and Ship B are 120 km apart when they pick up a distress call from another boat. Ship B estimates that they are 70 km away from the distress call. They also notice that the angle between the line from ship B to ship A and the line from ship A to the distress call is 28°. What are the two possible distances, to the nearest TENTH of a km, from ship A to the boat?

The two possible distance are 147.5km and 64.4km

Step-by-step explanation:

Given

See Attachment for Illustration

Required

Determine the possible distance of ship A from the boat

The distress is represented by X;

So, the question requires we calculate distance AX;

This will be done using cosine formula as follows;

In this case;

a = 70;

b = ??

x = 120

A = 28 degrees

Substitute these values in the formula above

Subtract 4900 from both sides

Solve using quadratic formula

Substitute 1 for a; -211.9 for b and 9500 for c

This can be splitted to

 or    

  or  

  or  

Hence, the two possible distance are 147.5km and 64.4km

part a: 1.08

part b: 27.59