ken leans a 12 foot ladder against his house . he places the ladder so that the base is 5 feet from the house. how far up the house does the ladder reach

Hey there!

First imagine this ladder as a right triangle, the length, 12 would be the slant height, the distance from the house, 5 would be the base length, and the height of how far up the ladder reaches would be the height of the triangle.

To represent this missing height, you can define it as the x variable.

Now, to solve for this x variable, you must use the Pythagorean theorem:
a^2+b^2=c^2

a and b are the two legs, and c is the slant length.

Now, plug in your known values:
(5)^2+(x)^2=(12)^2

Now, simplify:
25+x^2=144

Now, solve for x:
25+x^2=144
x^2=119
x=[tex] \sqrt{119} [/tex]
x is about 10.9.

Therefore, your final answer would be that the ladder reaches approximately 10.9 feet up the house.