Question

http://puu.sh/34HQy.png

Answer 1

Looks like a job for similar triangles...

Answer 2

Nope, that is the entire question right there.

Answer 3

What is the distance between yachts 2 and 3?

Answer 4

When you know that, you can set up similar triangles between harbor / yacht 2 / yacht 3 and yacht 1 / yacht 2 / harbor

Answer 5

49.

Answer 6

Okay, so how would you use that as I proposed?

Answer 7

Well actually there is a property of rigth triangles wicch is prooven with similarity.
Let x be the distance between Yacht 1 and harbor and in this case happens that
x^2 = 130*81
Now let y be the distance between yacht 2 and harbor
x^2=81^2 +y^2
(pythagorean theorem)
x^2=81^2 +y^2
130*81-81^2 = y^2
81(130-81)=y^2
y^2=81*49
y =9*7
y=63.

And that's the answer

Answer 8

The opposite is 49 from what I would see. That is all the information I have so far.

Answer 9

no need for Pythagoras:

if we call distance between yacht 2 and harbor \(x\), then because we have similar triangles, \[\frac{81}{x} = \frac{x}{49}\]Cross multiply:
\[x^2=81*49 = 9^2*7^2\]\[x=7*9=63\]

Answer 10

Give me a second for my brain to process these. xD

Answer 11

I don't understand where you got 9^2 and 7^2 from...

Answer 12

Oh wait, I see now... Nevermind. So what is the rule for you to be cross multiplying?

Answer 13

cross-multiplying is just a shortcut to solving:
\[\frac{a}{b}=\frac{c}{d}\]Multiply both sides by \(b\):
\[b\frac{a}{b} = b\frac{c}{d}\]Multiply both sides by \(d\):
\[bd\frac{a}{b} = bd\frac{c}{d}\]\[ad=bc\]

In other words, if the fractions are equal, then ad=bc.

Answer 14

Damn, I know how mathematical laws are just that. Laws. So I can just follow them without thinking about the logic behind them but I can't seem to solder it into my brain. :/