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A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 25 degrees. From a point 1225 feet closer to the mountain along the plain, they find that the angle of elevation is 30 degrees.
How high (in feet) is the mountain?

  • angles -

    make a sketch
    let the top of mountain be T
    base of mountain R
    so we want TR

    Let A be the point farthest from the top, let B be the closer point,
    AB = 1225
    In triangle TAB
    angle A = 25°
    angle TBR = 30° , so angle TBA =150°
    leaving us with angle ATB = 5°
    by the sine law:
    BT/sin25 = 1225/sin 5°
    BT = 1225sin25/sin5 = 5940.059

    so now in the right-angled triangle TBR
    sin 30 = TR/5940.059
    TR = 5940.059*sin30 = 2970.03 ft

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