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JEE Mains · Maths · STD 11 - Trigonometrical equations
A tower \(T_1\) of height \(60\, m\) is located exactly opposite to a tower \(T_2\) of height \(80\, m\) on a straight road. From the top of \(T_1\) . if the angle of depression of the foot of \(T_2\) is twice the angle of elevation of the top of \(T_2\), then the width (in \(m\)) of the road between the feet of the towers \(T_1\) and \(T_2\) is
- A \(20\sqrt 2 \)
- B \(10\sqrt 2 \)
- C \(10\sqrt 3 \)
- D \(20\sqrt 3 \)
Answer & Solution
Correct Answer
(D) \(20\sqrt 3 \)
Step-by-step Solution
Detailed explanation
Let the distance between \(T_1\) and \(T_2\) be \(x\) From the figure \(EA\, = \,60\,m\,({T_1})\) and \(DB\, = \,80\,m\,({T_2})\) \(\angle DEC\, = \,\theta \) and \(\angle BEC\, = \,2\theta \) Now in \(\Delta DEC,\) \(\tan \,\theta \, = \,\frac{{DC}}{{AB}}\, = \,\frac{{20}}{x}\)…
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