Question

"‘Skysails’ is that genre of engineering science that uses extensive utilization of wind energy to move a vessel in the sea water. The ‘Skysails’ technology allows the towing kite to gain a height of anything between 100 metres – 300 metres. The sailing kite is made in such a way that it can be raised to its proper elevation and then brought back with the help of a ‘telescopic mast’ that enables the kite to be raised properly and effectively.

Based on the following figure related to sky sailing, answer the questions:

(i) In the given figure, if sin θ = cos (3θ − 30º), where θ and (3θ − 30º) are acute angles, then find the value of θ.
(ii) What should be the length of the rope of the kite sail in order to pull the ship at the angle θ (calculated above) and be at a vertical height of 200 m?"

Answer 1

Answer:

θ  = 30º

Rope Length = 400  m

Step-by-step explanation:

sin θ = cos (3θ − 30º)

=> Cos (90 - θ ) = cos (3θ − 30º)

=> 90 - θ = 3θ − 30º    

=> 4θ  = 120º      

=> θ  = 30º

Sinθ = AB/AC

=> Sin30º = 200 / Rope Length

=> 1/2 = 200/ Rope Length

=> Rope Length = 400  m