Passenger boarding stairs, sometimes referred to as boarding ramps, stair cars or aircraft steps, provide a mobile…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 4 Marks · March 2025 · Standard
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304 Marks · March 2025 · Standard
Passenger boarding stairs, sometimes referred to as boarding ramps, stair cars or aircraft steps, provide a mobile means to travel between the aircraft doors and the ground. Larger aircraft have door sills 5 to 20 feet (1 foot = 30 cm) high. Stairs facilitate safe boarding and de-boarding. An aircraft has a door sill at a height of 15 feet above the ground. A stair car is placed at a horizontal distance of 15 feet from the plane. Based on given information, answer the questions given in part (i) and (ii). (i) Find the angle at which stairs are inclined to reach the door sill 15 feet high above the ground. (ii) Find the length of stairs used to reach the door sill. Further, answer any one of the following questions: (iii) (a) If the 20 feet long stairs is inclined at an angle of $60^\circ$ to reach the door sill, then find the height of the door sill above the ground. (use $\sqrt{3} = 1.732$) OR (iii) (b) What should be the shortest possible length of stairs to reach the door sill of the plane 20 feet above the ground, if the angle of elevation cannot exceed $30^\circ$? Also, find the horizontal distance of base of stair car from the plane.
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(i) $\tan \theta = \frac{15}{15} = 1 \implies \theta = 45^\circ$ (ii) $\frac{15}{l} = \sin 45^\circ \implies l = 15\sqrt{2}$ ft. or 21.21 ft. approx. (iii) (a) $\frac{h}{20} = \sin 60^\circ = \frac{\sqrt{3}}{2} \implies h = 10\sqrt{3} = 17.32$ ft. (iii) (b) $\frac{20}{l} = \sin 30^\circ = \frac{1}{2} \implies l = 40$ ft. $\frac{20}{x} = \tan 30^\circ = \frac{1}{\sqrt{3}} \implies x = 20\sqrt{3}$ ft. or 34.64 ft. approx.
