Solving right triangles; angles of elevation and depression
- The two reference lines — 3 tasks
- Plan the solve, compute nothing — 3 tasks
- Solving a right triangle — 3 tasks
- Elevation and depression — 3 tasks
- Going Deeper — 6 tasks
- Practice — 24 tasks
- Summary — 7 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.
-
Can It Be Found? Solving Right Triangles in Sightings — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 sightings in words: a kite string, a lighthouse keeper and a boat, a drone over a field, a tower seen from the ground. Students sort them with no calculation: the part asked can be found and needs sin, cos or tan; it can be found without them (90° minus an angle, or the Pythagorean theorem); or it cannot be found, because not enough is given (two angles, one length, or a length that is not a side of the triangle).
-
Which Angle Is It? Angles of Elevation and Depression — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a sighting in words with no drawing: a lighthouse keeper and a boat, a kite on its string, a drone over a field. Two lengths are given. Students find both acute angles of the right triangle and choose the one the question asks for: the angle of elevation or depression, measured from the horizontal line, or the angle against the vertical line. The row of box numbers at the foot is the check.
-
Elevation or Depression? Angles Measured from the Horizontal — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a small drawing of a sighting with one angle marked: an eye on a cliff looking down, an eye on the ground looking up at a tower. Is the marked angle the angle of elevation or depression from the eye, measured from the horizontal line? Or is it against the cliff, the wall or the tower? No numbers and no calculation: fill it or leave it white, and a picture appears.
-
Where Does the Angle Go? Angles of Elevation and Depression — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a sighting in words with no drawing: a lighthouse keeper and a boat, a drone and a cone, a kite on its string, a radio tower. Students draw the right triangle, put the angle of elevation or depression between the horizontal line and the line of sight, and find a length to the nearest foot. Putting the angle against the wall or the cliff instead lands on a card that sends the group back. A clean run is 8 lines on the record sheet.