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  • The angle of elevation of the top of a vertical tower from a point A, due east of it is 450.  The angle of elevation of the top of the same tower from a point B, due south of A is 3

The angle of elevation of the top of a vertical tower from a point A, due east of it is 450.  The angle of elevation of the top of the same tower from a point B, due south of A is 300.  If the distance between A and B is 54\sqrt{2}m , then the height of the tower (in metres), is :

Option: 1

36\sqrt{3}


Option: 2

54


Option: 3

54\sqrt{3}


Option: 4

108


Answers (1)

best_answer

As we learnt in

Height and Distances -

The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios.

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\\ A B=54 \sqrt{2} \\\\ \text{also using pythgoras we get} y^{2}=x^{2}+(54 \sqrt{2})^{2} \\\\ \text{angle }DAO =45^{\circ} \\\\ \tan 45=\frac{n}{x} \\\\ h=x_{----}(2)

\begin{aligned} &\angle DBO =30^{\circ}\\ &\tan 30=\frac{h}{y}\\ &\sqrt{3} h = y _{----}(3) \end{aligned}

\\ \operatorname{sub}\;\;(2)\;\; \& \;\; (3)\;\; \operatorname{in}\;\;(1) \text{ we get }\\\\ (\sqrt{3} h)^{2}=(h)^{2}+(54 \sqrt{2})^{2}\) \\\\h=54 m

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mansi

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