Fire tower A sites a fire in the direction North 20 degrees East. Tower B sites the same fire at North 35 degrees West. The towers are 4.2 km apart. The direction from tower B to tower A is North 72 degrees West. Find how far the fire is from each tower.

This kind of problem requires a diagram in order not to confuse oneself. After that, it straight-forward geometry and trigonometry.

Your job is to determine the length of YF and BF in the diagram.

Angle XAY is a right angle. Angle BXA is a right angle. Angle FYA is a right angle.

Angle XAB is 90 - 72 =18 degrees.

Angle FAX is 90 - 20 = 70 degrees.

Angle FAB is not a right angle (close -- 88 degrees). You know the length of AB in that triangle, and you also know all of the angles. You can solve for the lengths of the other sides using the law of sines. Once you know the length of line AF, you can calculate the triangle AYF (a right triangle) and solve for the length FY.

Try to go from there. If you still have problems, let me know and I'll help you with some other hints.