Question

Option 3

Option 4
A tree house is 10 feet up in a tree. A ladder that leans against the tree and
leads to the tree house door is 12 feet long. How far away from the base of
the tree is the bottom of the ladder? Draw a picture and solve. Round your
answer to the nearest tenth.

Answer 1

6.63 ft

Explanation:

In this case we use pythagora's theorem which is

`hyp^(2)` =
`adj^(2)` +
`opp^(2)`

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

`12^(2)` =
`adj^(2)` +
`10^(2)`

144 =
`adj^(2)` + 100

144 - 100 = 44 =
`adj^(2)`

the image is shown below

adj =
`√(44)` = 6.63 ft