ZIMSEC O Level · Mathematics · Form 3, Form 4
Trigonometry links the angles and sides of triangles.
Right-angled triangles
sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = opposite/adjacent (SOH CAH TOA).
Pythagoras: hypotenuse² = sum of the squares of the other two sides.
Worked example: A ladder 5 m long leans against a wall, making 70° with the ground. How high up the wall does it reach?
sin 70° = h/5 → h = 5 × 0.9397 = 4.70 m
Any triangle
- Sine rule: a/sin A = b/sin B = c/sin C.
- Cosine rule: a² = b² + c² − 2bc cos A.
- Area = ½ab sin C.
Worked example: In triangle PQR, p = 8 cm, q = 5 cm and angle R = 60°. Find r.
r² = 8² + 5² − 2(8)(5)cos 60° = 64 + 25 − 40 = 49 → r = 7 cm
Bearings
Bearings are measured clockwise from north and written with three figures, e.g. 045°, 230°. The back bearing differs by 180°.
Angles of elevation and depression
Measured from the horizontal: up to an object (elevation) or down to an object (depression).
Check yourself
- In a right-angled triangle, the hypotenuse is 13 cm and one side is 5 cm. Find the third side.
- The bearing of B from A is 070°. What is the bearing of A from B?
- Find the area of a triangle with sides 6 cm and 9 cm and included angle 30°.
Show answers
- 12 cm
- 250°
- ½ × 6 × 9 × 0.5 = 13.5 cm²
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