Question

A painter leans a 25-ft ladder against a building. The base of the ladder is 7 ft from the building. To the nearest foot, how high on the building does the ladder reach?
@DebbieG

Answer 1

@whalexnuker @DLS @FaithAnderson1997 @Christos @BulletWithButterflyWings @blondie16

Answer 2

It's just like the one you did yesterday:
http://openstudy.com/study#/updates/522dddf1e4b0a8663d5643a2

Just do the same way.

Answer 3

so a^2 +b^2=c^2

Answer 4

sure, if you like a, b and c better. I put the equation you need on the drawing above. :)

Answer 5

i got 49=625

Answer 6

Look, don't get hung up on the specific PROBLEM. it's a right triangle. In a right triangle:

(leg length)^2 + (leg length)^2 = (hypotenuse)^2

Answer 7

where's your h? (or a, or b, or whatever variable you are using for the height?)

Answer 8

There are THREE parts to the equation: 2 legs (one of which is the unknown here, so that has to be your variable), and the hypotenuse (the ladder length).

Answer 9

i just didnt type it . but h2+7^2=25^2
49=625

Answer 10

ok, we'll it's part of the equation... you can't just "leave it out"!! Then the equation doesn't make any sense, THAT'S the term with the variable that you are trying to solve for!

Now you have:

\(\Large h^2+7^2=25^2 \)
\(\Large h^2+49=625 \)

You want to solve for h, so you need to get that \(\Large h^2\) term all alone. What do you need to do next? What will "isolate" the \(\Large h^2\)?

Answer 11

subtract 49 from 625

Answer 12

Yes, good... you subtract the 49 from both sides. that effectively "MOVES" it from the left to the right, so the 2 sides are still equal.

and what do you get?

Answer 13

\(\Large h^2+49-49=625-49 \)
\(\Large h^2=? \)

Answer 14

-576 and sqrt it 24

Answer 15

wait..... why -576??

You can't take the sqrt of a negative number. Why did you get negative on RHS?

Be intuitive about it - don't just go through the motions! Surely you see that if you subtract 49 from 625, you will get a positive result?

Answer 16

i did it backwards i got 624 then sqrt it to get 24

Answer 17

I figured that's where the negative came from - it's fine to "do it backwards" like that (I often do that too) but just remember that your result is positive then. :)

But yes, after that, you are correct - take the square root of both sides.

\(\Large h^2=576 \)
\(\Large \sqrt{h^2}=\pm \sqrt{576} \)
\(\Large h=\pm 24 \)

Now, TECHNICALLY when you take the square root of both sides, you need to put that \(\pm\) in on the RHS, and you would get two solutions for h (the positive square root and the negative square root).

BUT, since this is an application problem, you can ignore the negative result - h here is a height, which can't be negative. But still worth noting that the equation does have two solutions, from a strictly algebraic standpoint.