An aeroplane when flying at a height of 3000 m from the ground passes vertically above another aeroplane at an instant…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · March 2023 · Standard
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375 Marks · March 2023 · Standard
An aeroplane when flying at a height of $3000$ m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are $60^{\circ}$ and $45^{\circ}$ respectively. Find the vertical distance between the aeroplanes at that instant. Also, find the distance of first plane from the point of observation. (Take $\sqrt{3} = 1.73$)
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1 mark for figure Let planes be located at points $C$ and $$\begin{aligned}& D \\ & \tan 45^{\circ} = 1 = \frac{3000 - h}{x} \Rightarrow x = 3000-h \quad \text{------(i)} \\ & \tan 60^{\circ} = \sqrt{3} = \frac{3000}{x} \Rightarrow x = 1000 \sqrt{3} \quad \text{------(ii)} \\ & \text{Using (i) and (ii) } h = 3000 - 1730 \\ & = 1270 \\ & \therefore \text{vertical distance between the aeroplanes } = 1270 \text{ m} \\ & \text{Also } \sin 60^{\circ} = \frac{\sqrt{3}}{2} = \frac{3000}{z} \Rightarrow z = 2000 \sqrt{3} = 3460 \\ & \text{Distance of the first plane from the point of observation } = 3460 \text{ m}\end{aligned}$$
