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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 2 · Set 1 · Q13
Case Study-1: Kite festival is celebrated in many countries at different times of the year. In India, every year 14^th January is celebrated as…
Case Study-$\displaystyle 1$ : Kite festival is celebrated in many countries at different times of the year. In India, every year $\displaystyle 14^{\text {th }}$ January is celebrated as International Kite Day. On this day many people visit India and participate in the festival by flying various kinds of kites. The picture given below, shows three kites flying together.
Fig. $\displaystyle 5$ In Fig. $\displaystyle 5$, the angles of elevation of two kites (Points A and B) from the hands of a man (Point C) are found to be $\displaystyle 30$° and $\displaystyle 60$° respectively. Taking $\displaystyle \mathrm{AD}=50 \mathrm{~m}$ and $\displaystyle \mathrm{BE}=60 \mathrm{~m}$, find
(1)
the lengths of strings used (take them straight) for kites A and B as shown in the figure.
(2)
the distance 'd' between these two kites
Marking-scheme solution
2.
\(\displaystyle \left.\begin{array}{c}\text { Since } D E \text { is a straight line therefore } \angle A C B=90^{\circ}
\therefore d^{2}=A C^{2}+B C^{2}=(100)^{2}+(40 \sqrt{3})^{2}\end{array}\right\}\)
\[\Rightarrow d=\sqrt{14800} \text { or } 20 \sqrt{37} \mathrm{~m}
\]
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