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Ex 9.1, 8 - A statue 1.6 m tall stands on top of a pedestal - Ex 9.1

EX 9.1, 8 - Part 2
EX 9.1, 8 - Part 3 EX 9.1, 8 - Part 4


Transcript

Ex 9.1 , 8 A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal. Here pedestal is AB & Statue is AC Height of pedestal = AB Length of the statue = 1.6m Hence, AC = 1.6m Angle of elevation to top of statue = 60° Hence, ∠CPB = 60° Angle of elevation at the top of the pedestal = 45° Hence, ∠APB = 45° We need to find height of pedestal i.e. AB Since statue is perpendicular to the ground ∠ ABP = 90° In ABP is a right triangle tan P = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝑃)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝑃) tan P = (" " 𝐴𝐵)/𝐵𝑃 tan 45° = (" " 𝐴𝐵)/𝐵𝑃 1 = (" " 𝐴𝐵)/𝐵𝑃 BP = AB Similarly, In a right angle triangle CBP tan P = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝑃)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝑃) tan P = (" " 𝐶𝐵)/𝐵𝑃 tan 60° = (" " 𝐶𝐵)/𝐵𝑃 √3 = (" " 𝐶𝐵)/𝐵𝑃 √3BP = CB √3AB = CB √3AB = AC + AB √3AB = 1.6 + AB √3AB – AB = 1.6 (√3−1)AB = 1.6 AB = 1.6/(√3 − 1)Rationalizing Multiplying (√3 " + 1)" in numerator and denominator AB = 1.6/(√3 − 1) × (√3 + 1)/(√3 + 1) AB = (1.6 × (√3 + 1))/((√3)^2 − 1^2 ) AB = (1.6 × (√3 + 1))/(3 −1) AB = (1.6 × (√3 + 1))/2 AB = 0.8 (√3 " + 1") Hence, Height of pedestal = AB = 0.8 (√3 " + 1") "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.