Case Study – 2 A class VI student went to a park and went up the slide to play. The angle of elevation of the slide is…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 4 Marks · July 2024 · Standard
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264 Marks · July 2024 · Standard
Case Study – 2 A class VI student went to a park and went up the slide to play. The angle of elevation of the slide is $30^{\circ}$, but the base from which the angle of elevation is measured is $50$ cm above the ground level and the distance of this point from the bottom of the staircase (which is vertical) is $4\sqrt{3}$ m. Based on the above information, answer the following questions: (i) Write the angle of depression from the top of the slide to its base. (ii) (a) Find the height of the staircase. OR (b) Find the length of the slide. (iii) Will the angle of elevation increase or decrease if the staircase was made taller?
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Sol. Let AB be the staircase. (i) $30^{\circ}$ (ii) (a) $\text{tan } 30^{\circ} = \frac{h-0.5}{4\sqrt{3}}$ $\Rightarrow h = 4.5$ So, height of the staircase is $4.5$ m OR (b) $\text{cos } 30^{\circ} = \frac{4\sqrt{3}}{l} = \frac{\sqrt{3}}{2}$ $\Rightarrow l = 8$ So, length of the slide is $8$ m. (iii) Angle of elevation will increase.
