JEE Main 2015 (Offline)Question 1
If the angles of elevation of the top of a tower from three collinear points $A$, $B$ and $C$, on a line leading to the foot of the tower, are $30^\circ$, $45^\circ$ and $60^\circ$ respectively, then the ratio, $AB:BC$, is :
Trigonometric Ratio & Identities
Solution
Concept. Write all three distances from the foot in terms of the height $h$. Formulas used. (1) Distance from the foot $=h\cot\theta$Step 1 - Distances. By (1): $A$ at $h\sqrt3$, $B$ at $h$, $C$ at $\frac{h}{\sqrt3}$. Step 2 - Gaps. $$AB=h(\sqrt3-1),\qquad BC=h-\frac{h}{\sqrt3}=\frac{h(\sqrt3-1)}{\sqrt3}.$$ Step 3 - Ratio. $AB:BC=\sqrt3:1$. Answer: (C)