MAth Igcse

The angle of elevation of the top of a tower is 27 degrees from point A due east of it. The angle of elevation of the top of the tower is 11 degrees from another point B due south of the tower. Find the height of the tower if the distance AB is 40m.

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  1. If we label the top of the tower T and the bottom Q, then we have

    tan 27° = PQ/QA
    tan 11° = PQ/QB
    QA^2 + QB^2 = 40

    (PQ/tan27°)^2 + (PQ/tan11°)^2 = 40^2
    Now just solve for PQ, the height of the tower.

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  2. Solving after steve's step:
    (PQ/tan27°)^2 + (PQ/tan11°)^2 = 40^2
    Take PQ^2 out as it is common to both:
    PQ^2(1/tan27^2 + 1/tan11^2)= 1600
    PQ^2=1600/(1/tan27^2 + 1/tan11^2)
    PQ=√1600/(1/tan27^2 + 1/tan11^2)
    PQ=7.26( 3 significant figures)

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