Answer:
6.63 ft
Step-by-step explanation:
In this case we use pythagora's theorem which is
[tex]hyp^{2}[/tex] = [tex]adj^{2}[/tex] + [tex]opp^{2}[/tex]
in this case, the hypotenuse (hyp) is the length of the ladder, the opposite (opp) is the height of the tree house and, the adjacent (adj) is the distance of the ladder's bottom to the base of the tree.
hpy = 12 ft
opp = 10 ft
adj = ?
substituting into the equation above, we have
[tex]12^{2}[/tex] = [tex]adj^{2}[/tex] + [tex]10^{2}[/tex]
144 = [tex]adj^{2}[/tex] + 100
144 - 100 = 44 = [tex]adj^{2}[/tex]
the image is shown below
adj = [tex]\sqrt{44}[/tex] = 6.63 ft
