Question
The angles of elevation of the top of a flagpole from
two points A and B on level ground are 30° and 60° respectively. The points A and B are on the same straight line as they are 20 meters apart. Find the height of the flagpole.Solution
Let the height of the flagpole be h meters, and let the distance of point A from the base of the pole be x meters. tan 30° = h/x. 1/√3 = h/x. h = x/√3. From the triangle formed with the 60° angle, tan 60° = h/(x - 20). √3 = h/(x - 20). h = √3(x - 20). Equating the two expressions for h: x/√3 = √3(x - 20). Multiply through by √3: x = 3(x - 20). x = 3x - 60. 2x = 60. x = 30 meters. Substitute x into h = x/√3: h = 30/√3 = 10√3 meters. Correct answer: a) 10√3 meters
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