Using the ratios to find a side length
- Judging the answer before you compute it — 3 tasks
- From the table to the calculator key — 3 tasks
- Where the unknown sits — 3 tasks
- Choosing the ratio — 3 tasks
- Going Deeper — 6 tasks
- Practice — 23 tasks
- Summary — 8 tasks
- Cool-down — 3 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
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Trig Ratios: Multiply or Divide? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 right triangles drawn to scale, each with one length and an x. Students do not compute: they name the sides from the given angle, pick the ratio, and sort each piece by its last step. Multiply (x on top of the fraction), divide (x underneath), or no angle is given at all, so the Pythagorean theorem is the tool.
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Trig Ratios: x on Top or Underneath? Finding a Side — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a right triangle drawn to scale with one acute angle, one side and an x. Students name the ratio, write the equation and find x to the nearest tenth. The wrong answers are the two costliest mistakes: multiplying where the equation divides, and mixing up opposite and adjacent. The row of box numbers at the foot is the check.
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Trig Ratios: Is the Equation Right? Finding a Side — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a right triangle drawn to scale with one angle, one length, an x and a finished equation such as x = 18 × sin 40°. Students compute nothing: they name the sides, pick the ratio and check whether x belongs on top or underneath. Fill it or leave it white, and a picture appears.
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Trig Ratios: Multiply or Divide? Finding a Side — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a right triangle drawn to scale with one acute angle, one side and an x. Students name the ratio, write the equation and find x to the nearest tenth, with x on top of the fraction on some cards and underneath on others. Multiplying where the equation divides, or mixing up opposite and adjacent, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.