Area of a triangle as one half ab sin C
- Two sides fixed, the angle moving — 3 tasks
- The height, produced by a sine — 3 tasks
- Where the sine comes from — 3 tasks
- The angle between the two sides — 3 tasks
- Going Deeper — 3 tasks
- Practice — 21 tasks
- Summary — 2 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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Area of a Triangle: Which Formula? ½ab sin C or Base × Height — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 triangles drawn to scale, some with a height marked, some with two sides and an angle. Students do not compute: they sort each piece by the formula that can find its area. One half base times height, ½ab sin C, or neither, because the marked angle is not between the two numbered sides.
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Area = ½ab sin C: Which Two Sides? Area of a Triangle Using Sine — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a triangle drawn to scale with all three sides labeled and one angle marked, some of them obtuse. Students pick the two sides that meet at the marked angle and find the area with ½ab sin C, to the nearest tenth. The wrong answers are the two commonest mistakes: using the side across from the angle, and leaving out the ½. The row of box numbers at the foot is the check.
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Area = ½ab sin C: Which Two Sides? Area of a Triangle Using Sine — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a triangle drawn to scale with all three sides labeled, one angle marked, and an expression for the area such as ½ × 9 × 14 × sin 44°. Students compute nothing: they find the two sides that meet at the marked angle and check whether the expression uses them. Fill it or leave it white, and a picture appears.
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Area = ½ab sin C: Which Two Sides? Area of a Triangle Using Sine — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a triangle drawn to scale with all three sides labeled and one angle marked, some of them obtuse. Students pick the two sides that meet at the marked angle and find the area with ½ab sin C, to the nearest tenth. Using the side across from the angle, or leaving out the ½, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.