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the angle of elevation from point on the ground to the top of a pyramid is 20 degrees 20 degrees the angle elevation from a point 189 feet farther back to the top of the pyramid is 10 degrees 20 degrees. find the height of the pyramid

  • math - ,

    Let A be the top of the pyramid,
    B = centre of pyramid at ground level

    P=position of first observation (angle=20 deg)
    Q=position of second observation (angle=10 degrees)

    Then PQ=189 feet

    and APQ is a triangle where
    APQ=10°
    AQP=180-20=160°
    Consequently PAQ=10 deg by angles of a triangle.
    Since triangle PAQ is an isosceles triangle, we deduce that PA=189 feet.
    and the height of the pyramid is
    h=189sin(20 deg).

    Note:
    This solutions takes advantage of the fact that the triangle is isosceles.
    In general, if it is not, the triangle can be solved using the sine rule, and h found consequently.

    If you have not done sine rule already, then you can let h=AB, and x=PB.
    Form two equations using each of the triangles APB and AQB in terms of h and x. Solve for h by eliminating x.

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