Maths · Trigonometrical identities and trigonometrical functions
From the top of a cliff height, a man observes the angle of depression of a boat
From the top of a cliff \( 24 \mathrm{mt} \) height, a man observes the angle of depression of a boat is to be \( 60^{\circ} . \) The distance of the boat from the foot of the cliff is
- A. \( 8 \sqrt{3} \mathrm{mt} \) t
- B. \( 8 \sqrt{2} \mathrm{mt} \)
- C. \( 8 \sqrt{5} \mathrm{m} \) t
- D. \( 8 \mathrm{m} \)
Step-by-step solution
Let distance of boat from foot of cliff be d. Angle of depression = 60°, so angle of elevation from boat to top of cliff = 60°. In right triangle, tan(60°) = opposite/adjacent = height/d = 24/d. Since tan60° = √3, we have √3 = 24/d => d = 24/√3 = 8√3 m.
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