From the top of a 60 m high building, the angles of depression of the top and bottom of a cable tower are observed to…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · July 2023 · Standard
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345 Marks · July 2023 · Standard
From the top of a $60$ m high building, the angles of depression of the top and bottom of a cable tower are observed to be $45^\circ$ and $60^\circ$ respectively. Find the height of the tower. (Use $\sqrt{3} = 1.73$)
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Sol. Correct figure (2 Marks) Let height of the tower be '$h$' m and ED = BC = '$x$' m In $\triangle AED$ $\frac{60-h}{x} = \tan 45^\circ = 1$ $\Rightarrow 60-h=x$ -----(1) (1/2 Mark) In $\triangle ABC$ $\frac{60}{x} = \tan 60^\circ = \sqrt{3}$ $\Rightarrow 60 = \sqrt{3} x$ (1/2 Mark) $\Rightarrow 60 = \sqrt{3} (60 - h)$ (1 Mark) $\Rightarrow h = 60 - \frac{60}{\sqrt{3}} = 60 - 20\sqrt{3} = 20(3-\sqrt{3})$ (1/2 Mark) $\Rightarrow h = 20 (3-1.73)$ $\Rightarrow h = 25.4$ (1/2 Mark) Hence, height of the tower is $25.4$ m.
