Analytical Geometry

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A 10 foot long ladder is leaning against a vertical wall with the top of the ladder 8ft from the ground. What is the slope of the ladder? How far is the foot of the ladder from the wall? Can a 6 foot tall man walk under the ladder 1 foot from the wall? Justify your answer.

  • Analytical Geometry -

    looks like plain ol' Pythagoras

    base^2 + 8^2 = 10^2
    bse^2 = 100-64 = 36
    base = √36 = 6
    slope = rise/run = height/base = 8/6 = 4/3

    Make a sketch of the situation
    Place the 6-ft man on the base 3 ft from the base.
    Is he below the ladder or did his head hit the ladder?
    Prove your conclusion with calculations.

  • Analytical Geometry -

    a soccer game is being televised by a certain tv station. a camera is situated 10 meters away from the longer side of the soccer field and 7 meters from the middle part.

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