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]
