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 ߠ = cos (3ߠ − 30଴ ), where ߠ and 3ߠ − 30଴ are acute angles, then find the value of ߠ. (ii) What should be the length of the rope of the kite sail in order to pull the ship at the angle ߠ) calculated above) and be at a vertical height of 200 m?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 ߠ = cos (3ߠ − 30଴ ), where ߠ and 3ߠ − 30଴ are acute angles, then find the value of ߠ. (ii) What should be the length of the rope of the kite sail in order to pull the ship at the angle ߠ) calculated above) and be at a vertical height of 200 m?

Answer 1

Answer:

(i) 30 degrees

(ii) 400 m

Step-by-step explanation:

For explanation, see the pictures.

Answer 2

Given : 'Skysails' technology allows the towing kite to gain a height of anything between 100 m to 300 m

Sin (θ)  = Cos(3θ - 30°)

To Find : Value of θ

Find rope length when vertical height =  200m

Solution:

Sin (θ)  = Cos(3θ - 30°)

=> Cos(90° - θ)  = Cos(3θ - 30°)

=> 90°  - θ = 3θ - 30°

=> θ = 30°

Sin(θ) = vertical height  / Rope Length

=> Sin  30°  = 200/ Rope Length

=> 1/2 = 200/ Rope Length

=> Rope length = 400 m

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