Examples
Last updated at April 16, 2024 by Teachoo
Example 3 An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45Β°. What is the height of the chimney? Here, In diagram AB is chimney and CD is observer. Angle of elevation = 45Β° Hence, β ADE = 45Β° And, Distance (BC) = 28.5m Height of observer = CD = 1.5 m Since BC & DE are parallel lines BC = DE = 28.5 m Also, CD & BE are parallel lines & CD = BE = 1.5 m We have to find height of chimney = AB Since chimney is perpendicular to ground β AED = 90Β° In right triangle AED, tan D = (ππππ πππππ ππ‘π π‘π πππππ" " π·)/(ππππ ππππππππ‘ π‘π πππππ" " π·) tan D = π΄πΈ/π·πΈ tan 45Β° = π΄πΈ/π·πΈ 1 = π΄πΈ/28.5 1 Γ 28.5 = AE AE = 28.5m Now, AB = AE + BE AB = 28.5 + 1.5 AB = 30m Hence, Height of chimney = AB = 30 metre