IIT-JEE 1983Question 1
From the top of a light-house $60$ metres high with its base at the sea-level, the angle of depression of a boat is $15^\circ$. The distance of the boat from the foot of the light house is
Trigonometric Ratio & Identities
Solution
Concept. The angle of depression equals the angle of elevation from the boat; distance $=60\cot15^\circ$. Formulas used. (1) $\cot15^\circ=2+\sqrt3=\dfrac{\sqrt3+1}{\sqrt3-1}$Step 1 - Distance. $60\cot15^\circ$. Step 2 - Match. By (1), $\frac{\sqrt3+1}{\sqrt3-1}=\frac{(\sqrt3+1)^2}{2}=2+\sqrt3$. So the distance is $\left(\dfrac{\sqrt3+1}{\sqrt3-1}\right)60$ m. Answer: (B)