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geometry

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Pine Tree In order to estimate the height h of a tall pine tree, a student places a mirror on the ground and stands where she can see the top of the tree, as shown. The student is 6 feet tall and stands 3 feet from the mirror which is 11 feet from the base of the tree. What is the height h (in feet) of the pine tree?

  • geometry -

    Can't see your diagram, but I know the question.
    You have similar triangles, so use ratios

    h/11= 6/3
    h = 11(2) = 22

  • geometry -

    let x height of pine tree.
    a=3 ,b=11, d=a+b, y=6 which is height of student. x=(dy-ay)/a ans.22
    not all the time ratio is applicable.

    alternate solution. you took the angle both triangle in terms of x, tangentx/d & tangentx/b. make an equation then substitute. ans still the same.

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