Answer:
4.9 feet
Step-by-step explanation:
First, we need to determine the height of the building using the following:
[tex]L^2 = H^2 + B^2[/tex]
Where
H = Height of the building
L = Length of the first ladder = 20ft
B = Distance from the base of the building = 10ft
So, we have:
[tex]20^2 = H^2 + 10^2[/tex]
[tex]400 = H^2 + 100[/tex]
[tex]H^2 = 400 - 100[/tex]
[tex]H^2 = 300[/tex]
[tex]H = \sqrt{300[/tex]
Next, is to determine the distance of the new ladder from the base of the building (B) using Pythagoras theorem using:
[tex]L_2^2 = H^2 + B_2^2[/tex]
Where
[tex]L_2 = 18[/tex] --- Length of the second ladder
[tex]H = \sqrt{300[/tex] ----- Height of the building
So, we have:
[tex]18^2 = \sqrt{300}^2 + B_2^2[/tex]
[tex]324 = 300 + B_2^2[/tex]
[tex]B^2_2 = 324 - 300[/tex]
[tex]B^2_2 = 24[/tex]
Solving for B2, we have:
[tex]B_2 = \sqrt{24[/tex]
[tex]B_2 = 4.9[/tex]
