3. From an island, the Titanic is 13 km away on a bearing of 80°.An iceberg is on a bearing of 125°from the titanic and 108° from the island. How far is the iceberg from the island?

Answer:9.61 kmStep-by-step explanation:See image while seeing explanationFirst we need to construct the figure, it is in the attached image.Now we start to put the different angles, in order to solve the triangle.Angle a is going to be the difference between 108° and 80°, giving 28°The angle between the distance from the island and the Titanic, and the line that goes to the east is going to be 10° as we subtract 90° and 80°. We trace a line (Co) between Where the titanic is and the line that goes to the east so it has 90° degrees between Co and E, after this, we know that having the Titanic as the center, the angle is 180°, so we subtract 180° and 125° to have part of angle b, 55°. Now we need to find the rest of the angle b, so, knowing that all triangles' angles sum 180°, 180° - 90° + 10° = 80°, that is the missing part of b, now we add those two parts and have that b= 135°. Now we can solve the triangle by  setting up an equation system:[tex]C^{2} =A^{2} + B^{2} - 2AB*Cos(b)\\\\B^{2}=C^{2} + A^{2} - 2AC*Cos(a)[/tex]We know the values of A, a and b, therefore, we replace those values and solve the system. As it is a second order equation system, we will have 2 different pairs of solutions:[tex]B_{1}=-20.87; C_{1}=31.44\\B_{2}=6.382; C_{2}=9.61[/tex]As a distance cannot be a negative number, we know that the proper solution is the second pair; in the triangle C is the distance between the island and the iceberg, givin 9.61 km