Question 24 - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Nov. 1, 2019 by Teachoo

‘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 sin𝜃 = cos (3𝜃 − 30°), where 𝜃 and 3𝜃 − 30° 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?

Question 24 ‘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 − 30°), where 𝜃 and 3𝜃 − 30° are acute angles, then find the value of 𝜃.
Given
sin 𝜃 = cos (3𝜃 − 30°)
Writing sin θ = cos (90° – θ)
cos (90° – 𝜃)= cos (3𝜃 − 30°)
Comparing angles
90° – 𝜃 = 3𝜃 − 30°
90° + 30° = 3θ + θ
120° = 4θ
4θ = 120°
θ = 120/4
θ = 30°
(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?
In Δ ABC
sin θ = 𝐴𝐵/𝐴𝐶
sin 30° = 200/𝐴𝐶
1/2 = 200/𝐴𝐶
AC = 2 × 200
AC = 400 m
So, length of the rope is 400 m

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.