Sides at Any Angle

The angles 30°, 45° and 60° have tidy ratios, but most angles do not. A slide 12 m long makes 37° with the ground. How high is its top? The height is opposite 37° and the slide is the hypotenuse, so the sine links them.

The board writes sin(37°) = x/12. Multiply both sides by 12: x = 12sin(37°). That is the exact answer, but nobody can measure 12 sin 37° with a tape. A calculator in degree mode gives sin 37° = 0.6018..., so x is about 7.22 m.

On the board the last step is a chip: Round to 2 decimal places turns the exact line into a number. The lesson says how many places it wants, and the answer must have exactly that many.