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Math-trig

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A stairway runs up the edge of the
pyramid. From bottom to top the stairway
is 92 m long. The stairway makes an angle of 70° to the base edge, as shown. A line from the middle of one of the base edges to the top of the pyramid makes an angle of elevation of 52° with respect to the flat ground. Find the height of the pyramid.

I just can't figure out where 70 degrees comes into play, help is appreciated :)

  • Math-trig -

    I can't see how this makes sense. Apparently the staircase runs up along one edge of the pyramid. Since the edge is longer than the altitude of one of the faces, its angle of elevation must be less.

    Better describe the diagram. Be sure to mark and label all points and edges of interest.

  • Math-trig -

    Wait. I see it.

    One face of the pyramid is an isosceles triangle with base angles of 70°

    So, the altitude of one of the faces is 92 sin70°, and half the base of one face is 92 cos70°

    so, if h is the pyramid height,

    sin52° = h/(92sin70°)
    h = 68.12

    or,
    tan52° = h/(92cos70°)
    h = 40.27

    Hmmm. I have messed up somewhere; maybe you can straighten it out.

  • Math-trig -

    Thanks so much!!

  • Math-trig -

    The question in the textbook misses key information

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