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Ex 9.1, 3 - A contractor plans to install two slides for - Ex 9.1

EX 9.1, 3 - Part 2
EX 9.1, 3 - Part 3 EX 9.1, 3 - Part 4


Transcript

Ex 9.1 , 3 A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case? Let smaller slide be represented by right angle triangle ABC. Here, Height of small slide = 1.5m So, AB = 1.5m Also it is inclined at an angle of 30° to the ground. Hence, ∠ACB = 30° We need to find the length of slide i.e. AC. In right angled triangle ABC sin C = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐶" " )/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 sin 30° = 𝐴𝐵/𝐴𝐶 1/2 = 1.5/𝐴𝐶 1 × AC = 1.5 × 2 AC = 3 m So, Length of small slide = 3m Similarly, we can do for larger slide Let larger slide be represented by right angle triangle PQR. Height of large slide = 3m So, PQ = 3m Also it is inclined at an angle of 60° to the ground. Hence, ∠PRQ = 60° We need to find the length of slide i.e. PR. In right triangle PQR sin R = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝑅" " )/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 sin R = 𝑃𝑄/𝑃𝑅 sin 60° = 3/𝑃𝑅 √3/2 = 3/𝑃𝑅 PR = (3 × 2)/√3 PR = (3 × 2)/√3 × √3/√3 = (6√3)/3 = 2√3 So, length of big slide = 2√3 m

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.