JEE Advance - Mathematics (1982 - No. 37)
A vertical pole stands at a point $$Q$$ on a horizontal ground. $$A$$ and $$B$$ are points on the ground, $$d$$ meters apart. The pole subtends angles $$\alpha $$ and $$\beta $$ at $$A$$ and $$B$$ respectively. $$AB$$ subtends an angle $$\gamma $$ and $$Q$$. Find the height of the pole.
$$\frac{d}{\sqrt{\cot^2 \alpha + \cot^2 \beta + 2\cot \alpha \cot \beta \cos \gamma}}$$
$$\frac{d}{\sqrt{\cot^2 \alpha + \cot^2 \beta - 2\cot \alpha \cot \beta \cos \gamma}}$$
$$\frac{d}{\sqrt{\cot^2 \alpha + \cot^2 \beta - \cot \alpha \cot \beta \cot \gamma}}$$
$$\frac{d}{\sqrt{\cot^2 \alpha - \cot^2 \beta - \cot \alpha \cot \beta \cos \gamma}}$$
$$\frac{d}{\sqrt{\tan^2 \alpha + \tan^2 \beta - \tan \alpha \tan \beta \cos \gamma}}$$