A) \[\frac{a+b}{a-b}\]
B) \[\frac{a-b}{a+b}\]
C) \[\sqrt{ab}\]
D) \[{{(ab)}^{1/3}}\]
Correct Answer: C
Solution :
Let there are two points C and D on horizontal line passing from point B of the base of the tower AB. The distance of these points are b and a from B respectively. \[\therefore BD=a\,\,\text{and}\,\,BC=b\]. \[\because \] line CD, on the top of tower A subtends an angle \[\theta \], \[\therefore \,\,\angle CAD=\theta \] According to question, on point C and D, the elevation of top are \[\alpha \] and \[{{90}^{o}}-\alpha \]. \[\therefore \,\,\,\,\angle BCA\,\,\,\,=\,\,\,\alpha \] and \[\,\,\angle BDA=\]\[{{90}^{o}}-\alpha \]. In \[\Delta ABC,\] \[AB=BC\tan \alpha \] \[=b\tan \alpha \] ?.. (i) and in\[\Delta ABD\], AB = BD\[\tan ({{90}^{o}}-\alpha )\]\[=a\cot \alpha \] ?..(ii) Multiplying equation (i) and (ii), \[{{(AB)}^{2}}=(b\tan \alpha )(a\cot \alpha )=ab\], \[\therefore \,AB=\sqrt{(ab)}\].You need to login to perform this action.
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