Case Study - 1:

**Kite Festival**

Kite festival is celebrated in many countries at different times of the year. In India, every year $14^{th}$ January is celebrated as International Kite Day. On thi

Question

Case Study - 1:

**Kite Festival**

Kite festival is celebrated in many countries at different times of the year. In India, every year $14^{th}$ 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.

[IMAGE_1]

In Fig. 5, the angles of elevation of two kites (Points A and B) from the hands of a man (Point C) are found to be $30°$ and $60°$ respectively. Taking $AD = 50$ m and $BE = 60$ 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.

Accepted Answer

Step 1: (1) $\sin 60° = \frac{\sqrt{3}}{2} = \frac{60}{BC} \Rightarrow BC = 40\sqrt{3}$ m
Step 2: $\sin 30° = \frac{1}{2} = \frac{50}{AC} \Rightarrow AC = 100$ m
Step 3: (2) Since $DE$ is a straight line, $\angle ACB = 90°$. $d^2 = AC^2 + BC^2 = (100)^2 + (40\sqrt{3})^2 = 10000 + 4800 = 14800$
Step 4: $d = \sqrt{14800} = 20\sqrt{37}$ m

Question

Solution