JEE Mains · Maths · STD 11 - Trigonometrical equations
A spherical gas balloon of radius \(16\, meter\) subtends an angle \(60^{\circ}\) at the eye of the observer \(A\) while the angle of elevation of its center from the eye of \(A\) is \(75^{\circ}\). Then the height (in \(meter\)) of the top most point of the balloon from the level of the observer's eye is:
- A \(8(\sqrt{2}+2+\sqrt{3})\)
- B \(8(\sqrt{6}+\sqrt{2}+2)\)
- C \(8(2+2 \sqrt{3}+\sqrt{2})\)
- D \(8(\sqrt{6}-\sqrt{2}+2)\)
Answer & Solution
Correct Answer
(B) \(8(\sqrt{6}+\sqrt{2}+2)\)
Step-by-step Solution
Detailed explanation
\(\mathrm{O} \rightarrow\) centre of sphere \(\mathrm{P}, \mathrm{Q} \rightarrow\) point of contact of tangent from \(\mathrm{A}\) Let \(\mathrm{T}\) be top most point of balloon \(\&\) \(\mathrm{R}\) be foot of perpendicular from \(\mathrm{O}\) to ground. From triangle…
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