Akhil is flying a kite with a rope of length 129 \(m\) from a building of height 19 \(m\) above the ground. He observes the kite at an angle of 30\(^{\circ}\). His friend Kumar observes the kite at an angle of 45\(^{\circ}\) from the ground. If they both are on the opposite sides of the kite, find the distance of the kite from Kumar. (Use \(\sqrt{3} = 1.732\) and \(\sqrt{2} = 1.414\))
Answer:
Let \(A\) and \(B\) denote the position of Kumar and Akhil, respectively.
Let \(AE\) denote the distance between the two friends Akhil and Kumar.
Let \(AC\) denote the distance of the kite from Kumar.
Let \(BC\) denote the length of the rope and \(BE\) denote the height of the building.
In the right \(\triangle CFB\), \(sin \ 30^{\circ} =\)
\(CF=\)\(m\)
\(CD = \)\(m\).
In the right \(\triangle CDA\), \(sin \ 45^{\circ} = \)
The distance of the kite from Kumar is .
(Note: Round off the answer to \(2\) decimal places.)