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Year 9–10 · Year 9–10 Maths

Year 9–10 Maths — Trigonometry

Trigonometry introduces sin, cos and tan as ratios in right-angled triangles, then extends to non-right triangles using the sine and cosine rules. These concepts carry directly into VCE Methods and Physics. Understanding when to use each rule — and how to find angles as well as sides — is the key skill.

Key Concepts & Formulas

  • SOHCAHTOA: sin θ = Opposite/Hypotenuse; cos θ = Adjacent/Hypotenuse; tan θ = Opposite/Adjacent

  • To find a side: rearrange the trig ratio for the unknown side

  • To find an angle: use the inverse trig function: θ = sin⁻¹(O/H) etc.

  • Pythagoras: a² + b² = c² — use for the hypotenuse; only works in right-angled triangles

  • Sine rule: a/sin A = b/sin B = c/sin C — use when you know one side-angle pair + one other side or angle

  • Cosine rule: c² = a² + b² − 2ab cos C — use when you know two sides and the included angle, or all three sides

  • Area of a triangle: A = ½ab sin C (when two sides and the included angle are known)

  • Angles of elevation: measured upward from the horizontal; angles of depression: measured downward from the horizontal

  • Exact values: sin 30° = ½, cos 30° = √3/2, tan 30° = 1/√3; sin 45° = cos 45° = 1/√2; sin 60° = √3/2

Practice Questions

5 questions

Attempt each question before reading the hint. These are styled to match school assessment format.

Q1.A right triangle has hypotenuse 13 cm and one leg of 5 cm. Find the angle opposite the 5 cm leg.

2 marks

Q2.A ladder 8 m long leans against a wall at an angle of 65° to the ground. Find how far up the wall it reaches.

2 marks

Q3.In triangle ABC, a = 7, b = 9 and C = 52°. Find side c using the cosine rule.

3 marks

Q4.Find the area of a triangle with sides 6 cm and 9 cm and an included angle of 40°.

2 marks

Q5.From the top of a 60 m cliff, the angle of depression to a boat is 28°. Find the horizontal distance from the cliff to the boat.

3 marks

Common Mistakes to Avoid

These are the errors that students most frequently make in Trigonometry — and that examiners are specifically watching for.

  • Applying SOHCAHTOA to a non-right triangle — use the sine or cosine rule instead

  • Using the angle of depression directly as the angle in the triangle — draw a diagram first

  • Choosing the wrong trig rule: use sine rule for angle-side-angle or side-side-angle; cosine rule for side-angle-side or side-side-side

  • Calculator in wrong mode: make sure degrees mode is on unless the question specifies radians

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