Solve application problem

Question

A guy wire bracing a tower is 20m long and makes a 50 degree angle with the ground. It is to be replaced by a 30m wire starting from the same point on the ground. How much further up the tower will the new wire reach?

Answer 1

Draw a figure!

The anchor point is 20 cos 50 from the base.

The first wire is attached 20 sin 50 up the tower.

The angle of inclination of the 30 m wire is given by arccos (2/3) sin 50

And the point at which the longer wire is attached is 30 sin arccos (2/3) sin 50

The distance required by the problem is the difference between the attachment points.

I seem to remember that there is an easier way to do this problem...but right off I can't remember it!