Question

24 'Skysails' is that genre of engineering science that uses extensive utilization of wind 2
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:
Ropc
(0)
In the given figure, if sin 8 = cos (30 - 30°), where 9 and 30 -- 30° are acute
angles, then find the value of 0.
What should be the length of the rope of the kite sail in order to pull the ship at
the angle 9 (calculated above) and be at a vertical height of 200 m2​

Answer 1

Answer:

30 degree and 400 m

Step-by-step explanation:

(i) 30⁰ (ii) 400 m

Given – sin Ө = cos (3Ө − 30⁰) & AB = 200 m

To find – Ө & AC

Property – sin Ө = cos (90⁰ - Ө)

Answer –

Given equation, sin Ө = cos (3Ө − 30⁰)

As sin Ө = cos (90⁰ - Ө), therefore,

cos (90⁰ - Ө) = cos (3Ө − 30⁰)

∴ 90⁰ - Ө = 3Ө − 30⁰

∴ 4Ө = 120⁰

∴ Ө = 30⁰

Hence, the value of Ө is 30⁰.

Now, in right-angled triangle ABC,

sin Ө= AB/AC

1/2= 200/AC

∴ AC = 400

Hence, the length of the rope of the kite is 400 m.

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Answer 2

Answer:

(i) 30 degrees

(ii) 400 m

Step-by-step explanation:

For explanation, see the pictures.