Answer:
9.61 km
Step-by-step explanation:
See image while seeing explanation
First 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
