L7 · Trigonometry clinic

Learning goal

“I can look at any right-triangle problem in this unit — naming ratios, finding a side, finding an angle, solving completely, elevation/depression, or two triangles — and select the correct first move without being told which lesson it came from.”

First move — the decision that starts every problem: name the sides relative to the marked angle, then pick Pythagoras, a ratio, an inverse, the complement, or the shared side.

Audit — the closing check: legs² vs hypotenuse², angle sum 180°, bigger angle facing the bigger leg, and the hypotenuse longer than every leg.

Worked example

Four mini-problems, sorted aloud: (a) Hypotenuse 34, angle 57°, find the opposite side -> ratio (x on top): 34 × sin 57°. (b) Legs 20 and 21, find the hypotenuse -> Pythagoras: √(400 + 441) = 29. (c) Opposite 11, adjacent 11, find the angle -> inverse: tan⁻¹(1) = 45°. (d) Angle 18°, hypotenuse 34, both legs wanted -> complement + ratios: other angle 72°; legs = 34 × sin 18° ≈ 10.5 and 34 × cos 18° ≈ 32.3. Say it plainly: every problem in this unit is one of five first moves. The numbers are the easy part; the sort is the skill.

Check yourself — explain it

A problem gives one leg and the hypotenuse and asks for an angle. Why is 'ratio' the wrong pile?

Paired problem — example still visible

Sort and start: Legs 8 and 15; find the angle opposite the 8 leg. -> Inverse (after optional Pythagoras): tan⁻¹(8/15) ≈ 28° — no hypotenuse needed.

Faded completion — last step is yours

"First move: ratio, unknown on top. Hypotenuse 80 m of kite string, angle 70°: height = 80 × sin 70° = ___ m." -> 75.2 m

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz

Grade 10 — Mathematics 10C › C10U03 Trigonometry of Right Triangles

L7 · Trigonometry clinic