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A road runs from the base of a mountain. From two points 235 meters apart on the road, the angles of elevation to the top of the mountain are 43 and 30. how high above the road is the mountaintop?

  • trig -

    Draw a diagram. If the nearer point is a distance x from the base of the mountain, then the height h can be figured from

    h/x = tan 43°
    h/(x+235) = tan 30°

    x = h/tan 43°
    x = h/tan 30° - 235

    h/tan 43° = h/tan 30° - 235
    h = 235/(cot30° - cot43°)
    h = 356.2 m

    not much of a mountain.

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