Question

A ladder is leaning against a brick chimney as shown in the picture below. The ladder is 25 feet long and is placed 15 fee up on the chimney. In order for the ladder to be stable, its base must be 15 feet or less away from the base of the chimney. Is the current position of the ladder stable?

A. No, the distance of the ladder from the base of the chimney is 20 feet.

B. No, the distance of the ladder from the base of the chimney is 40 feet.

C. Yes, the height of the ladder and the distance from the base of the chimney are both 15 feet.

D. Yes, the distance of the ladder from the base of the chimney is 10 feet.

Answer 1

Letter A.

Explanation:

The Pythagorean theorem formula is
`a^(2)+b^(2)=c^(2)`. The length of the hypotenuse, the longest side, is your
`c` value. The lengths of the legs If you substitute 25 for
`c` and 15 for
`a`, you would get
`15^2 +b^2=25^2`.
`25^2` equals
`625` and
`15^2` equals
`225`, so you would get
`225 +b^2=625`.
`625-225=400`, so
`b^2=400`. If you take the square root of both sides, you would get
`b=20ft`. Since the base of the ladder has to be fifteen feet or less away from the base of the chimney and
`15ft\\geq20ft`, the ladder is therefore unstable.

Answer 2

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=√(c^2 - o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{25}\\ a=\stackrel{adjacent}{b}\\ o=\stackrel{opposite}{15} \end{cases} \\\\\\ b=√( 25^2 - 15^2)\implies b=√( 625 - 225 ) \implies b=√( 400 )\stackrel{ \textit{the ladder is not stable} }{\implies \boxed{b=20}}`