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
Question
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 coneshaped building is 50 feet, and the radius of its base is 20 feet. Find the building's slant height. Show all work
1 Answer

1. User Answers calculista
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]
Stepbystep 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=24^212^2[/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]