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  • A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. After covering a distance of 50 m, the angle o

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. After covering a distance of 50 m, the angle of depression of the car becomes 60°. Find the height of the tower .\left ( Use {\sqrt{3}=1.73 } \right )

 
 
 

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\\\text { Let height of tower be } \mathrm{h} \ \mathrm{m} \text { and } \mathrm{BC}=\mathrm{x} \ \mathrm{m}\\ $In triangle ABC $ \\ \tan 60^{\circ}=\frac{\mathrm{h}}{\mathrm{x}}\\\\ \mathrm{h}=\sqrt{3} \mathrm{x}.....(i)\\ $In triangle ABD $\\\tan 30^{\circ}=\frac{\mathrm{h}}{\mathrm{x}+50}\\\\ x+50=\sqrt{3} h.......(ii)\\ $From equation (I) \& (ii)$ \\ x + 50 = \sqrt{3} \sqrt{3}x \\ 2x =50 \\ x =25 \ m \\

h = 25\sqrt{3} \ m \\

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