Students will see how the difference formula for tan can be used to find the acute angle between two lines, firstly, when neither line is vertical, then when exactly one line is vertical. Watch this, then this, to understand how to deliver this lesson.
Concude by giving your students this challenge:
Different Deductions by NRICH: Here's how I solved this puzzle: Look at the first column and third column, they are the same, except the first column contains a triangle in the first row, while the third column contains a square in the first row. This tells us we have to find how the value of the triangle and square differ. But have a look at the third and fourth rows. They only differ in that one contains a triangle while the other contains a square. But the sum of these rows is known, so from this, we deduce the value of the triangle is 2 less than the value of the square. Thus, the sum of the first column must be 2 less than the sum of the third column. So our answer must be 23 - 2 = 21. You could also solve this puzzle by determining the value of each shape, but as I've just shown, this isn't necessary.