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Example 4 - From a point P on the ground angle of elevation - Examples

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Example 4 From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff and the distance of the building from the point P. (You may take √3 = 1.732)? Given Height of building = 10 metre. So, BA = 10m Angle of elevation from point P to the top of the building = 30° So, ∠ BPA = 30° Angle of elevation from point P to the top of flag = 45° So, ∠ DPA = 45° We have to find out the length of the flag i.e. DB. And, distance of the building from the P i.e. PA Since building is vertical to ground ∴ ∠ BAP = 90° In right angle triangle BAP, tan P = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" P " )/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝑃) tan 30° = (" " 𝐵𝐴)/𝑃𝐴 1/√3 = (" " 10)/𝑃𝐴 1 × PA = 10 × √3 = 10 × 1.732 = 17.32 m PA = 10 √3 Hence, Distance of the building from point, P = 17.32 m Similarly, In right angle triangle DPA, tan P = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝑃)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝑃) tan 45° = 𝐷𝐴/𝑃𝐴 1 = 𝐷𝐴/𝑃𝐴 1 = (𝐷𝐵 + 𝐵𝐴)/𝑃𝐴 PA = DB + BA 10√3 = DB + 10 DB = 10√3 – 10 DB = 10 (√3 – 1)= 10 × (1.732 − 1) = 10 × 0.732 = 7.32 m Hence, length of the flagstaff = DB = 7.32 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.