Trigonometry — O/L Mathematics

How do I practise Trigonometry?

1 question with a worked solution

1. From the top of a 30-metre vertical cliff, the angle of depression of a boat out at sea is 30°. How far is the boat from the foot of the cliff? (Use tan 30° = 1/√3)
   1. A) 30 m
   2. B) 30√3 m (approx. 51.96 m)
   3. C) 60 m
   4. D) 15√3 m
   Check my answer

   Correct answer: B) 30√3 m (approx. 51.96 m)

   Angle of elevation from boat to cliff top = angle of depression = 30° (alternate angles). tan 30° = opposite / adjacent = 30 / d → 1/√3 = 30 / d → d = 30√3 metres.

   Show worked solution

   Step 1: Identify alternate angle: angle of depression = angle of elevation from boat = 30°. Step 2: Trigonometric ratio: tan(30°) = Height / Distance = 30 / d. Step 3: Solve for d: d = 30 / tan(30°) = 30 / (1/√3) = 30√3 m ≈ 51.96 m. Answer: 30√3 m (approx. 51.96 m).
   Modelled on: the O/L Mathematics examination pattern

Get this auto-marked

Next in the syllabus

Where does Trigonometry fit in the syllabus?

Grade 11 · Term 3