Mathematics

Question

1. The science club constructed a pyramid with a square base out of paper clips. The height of the pyramid is 2.5 feet. One side of the square measures 2.5 feet. What is the slant height of the pyramid?

2. A modern skyscraper is being built with triangular shaped windows. One window is a right triangle with the longest side measuring 24 inches and another side measuring 12 inches. What is the length of the third side of the window?

3. The height of a cone-shaped building is 50 feet, and the radius of its base is 20 feet. Find the building's slant height. Show all work

1 Answer

  • Answer:

    Part 1) The slant height of the pyramid is [tex]2.80\ ft[/tex]

    Part 2) The length of the third side of the window is [tex]20.78\ in[/tex]

    Part 3) The building's slant height is [tex]53.85\ ft[/tex]

    Step-by-step explanation:

    Part 1) we know that

    To find out the slant height of the pyramid, apply the Pythagorean Theorem

    Let

    l ----> the slant height of the pyramid

    h ---> the height of the pyramid

    b ---> the length side of the square base

    [tex]l^2=h^2+(b/2)^2[/tex]

    we have

    [tex]h=2.5\ ft\\b=2.5\ ft[/tex]

    substitute the given values

    [tex]l^2=2.5^2+(2.5/2)^2[/tex]

    [tex]l^2=2.5^2+(1.25)^2[/tex]

    [tex]l^2=7.8125[/tex]

    [tex]l=2.80\ ft[/tex]

    Part 2) Let

    c ----> the hypotenuse of a right triangle (the greater side)

    a ---> the measure of one leg of the right triangle

    b ---> the measure of the other leg of the right triangle

    Applying the Pythagorean Theorem

    [tex]c^2=a^2+b^2[/tex]

    we have

    [tex]c=24\ in\\a=12\ in[/tex]

    substitute the given values and solve for b

    [tex]24^2=12^2+b^2[/tex]

    [tex]b^2=24^2-12^2[/tex]

    [tex]b^2=432[/tex]

    [tex]b=20.78\ in[/tex]

    Part 3) Let

    l ----> the building's slant height

    h ---> the height of the building

    r ---> the radius of the base of the building

    Applying the Pythagorean Theorem

    [tex]l^2=h^2+r^2[/tex]

    we have

    [tex]h=50\ ft\\r=20\ ft[/tex]

    substitute the given values

    [tex]l^2=50^2+20^2[/tex]

    [tex]l^2=2,900[/tex]

    [tex]l=53.85\ ft[/tex]

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