A 3m long ladder is leaned on a wall so that the foot of the ladder is 1m from the base of the wall. How high up the wall does the ladder reach?

Question

anonymous · Answer

|dw:1414929833742:dw|

Do you know what you need to apply here?

anonymous · Answer

That's what I need to find out.. I have an idea.
X² = 1m² + 3m²
X² = 1m + 9m
X = 10m 
X = √10m
X = 3.1622776601683793319988935444327
X = 3.16 (2DP)

anonymous · Answer

@Joq

anonymous · Answer

You're in the right path. Let me help you a little bit.

anonymous · Answer

You already know that by using the Pythagorean Theorem we can solve the problem:

$\large{a^2= b^2 + c^2}$

$a$ is the hypotenuse, and $b$ and $c$ are the shortest sides. In this case, the hypotenuse is the ladder, and we also have the length of one of the shortest sides (the length made by the bottom of the ladder with the wall), let call it $b$. So we need to find $c$:

$\large{a= 3\ m}$
$\large{b= 1\ m}$
$\large{c= \ ?\ m}$

$\large{(3\ m)^2= (1\ m)^2 + c^2}$

Then I think you can solve for c.

anonymous · Answer

You just need to isolate $c$ and do the same thing you do above, and you're done.

anonymous · Answer

Do you think you could explain this a bit better? I'm 14.

anonymous · Answer

@Joq

anonymous · Answer

Sure! Let me try.

anonymous · Answer

In our problem, $a$ and $b$ are the knowns, and we need to find $c$. 

In order to find $c$ we need to isolate it in one side of the equation, to say, in the right-hand side, because we know that in the left-hand side its value is going to show up (since there are no more unknowns). How do we do that? 

We have:

$\large{a^2= b^2 + c^2}$

$\large{a^2-b^2= c^2}$ <- Subtract $b^2$ from both sides.

$\large{\sqrt{a^2-b^2}= c}$ <- Take the inverse operation of an exponent to the 2nd power, which is a square root, in order to find the result of $c$ and not $c^2$.

If we try to do this: $a = \sqrt{b^2 + c^2}$ it's like trying to find the hypotenuse, but by looking at the drawing, we do know the hypotenuse, which is 3m: the ladder.

anonymous · Answer

So I'd work it out like this:

X² = 3m² - 1m²
X² = 9m - 1m
X = 8m
X = √8m
X = 2.8284271247461900976033774484194
X = 2 (NWN)
@Joq

anonymous · Answer

Yep!. Exactly.

anonymous · Answer

I think the answer can be rounded to 2 decimal places ($2.83\ m $) or written with the square root ($2\sqrt{2}\ m)$.

anonymous · Answer

Thank-you ever so much. That really helped a lot. Thanks :-)

anonymous · Answer

@Joq

anonymous · Answer

You're very welcome @ellieearnshaw  (: