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?

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:

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:

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

180-142=38 for the acute angle next to the entry

90+38=128

180-128=52

a=52

step-by-step explanation:

this linear equation would have just one solution.

step-by-step explanation:

the reason why this would have one solution is that it is an expression with just one variable. since that variable is not raised to a power, it will always have just one solution.