Answer
Distance of top of the ladder to the base of the house is\[13.22\text{ feet}\].
Work Step by Step
The figure shows that the height of ladder is 20 feet and the distance of base ladder from the house is 15 feet. The distance of the top of the ladder to the base of the house is x.
Let c be the height of ladder and b be the distance of base ladder from the house. Hence, \[c=20\]and\[b=15\].
Compute the value of \[c\]by using Pythagorean Theorem and substitute the value of a and b into\[{{c}^{2}}={{a}^{2}}+{{b}^{2}}\]as shown below.
\[\begin{align}
& {{c}^{2}}={{a}^{2}}+{{b}^{2}} \\
& {{20}^{2}}={{a}^{2}}+{{15}^{2}}
\end{align}\]
Now if\[{{20}^{2}}=20.20=400\]and\[{{15}^{2}}=15.15=225\]complete the equation as follows:
\[400={{a}^{2}}+225\]
Subtract 225 from both sides to compute as shown below:
\[\begin{align}
& {{a}^{2}}=400-225 \\
& {{a}^{2}}=175 \\
& \sqrt{{{a}^{2}}}=\sqrt{175} \\
& a=13.22
\end{align}\]
