A pole 6 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point P…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · March 2024 · Standard
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495 Marks · March 2024 · Standard
A pole $6$m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point P on the ground is $60^\circ$ and the angle of depression of the point P from the top of the tower is $45^\circ$. Find the height of the tower and the distance of point P from the foot of the tower. (Use $\sqrt{3} = 1.73$)
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Sol. Correct figure Let BC be the pole and AB be the tower of height '$h$' m. $\tan 45^\circ = 1 = \frac{h}{x}$ $\Rightarrow h = x$ ----- (i) $\tan 60^\circ = \sqrt{3} = \frac{h+6}{x}$ $\Rightarrow h + 6 = x\sqrt{3}$ ----- (ii) Solving (i) & (ii) to get $h = 3 (\sqrt{3} + 1) = 8.19$ and $x = 8.19$ Therefore, the height of tower is $8.19$ m and the distance of point P from the foot of the tower is $8.19$ m
