Question

http://prntscr.com/j01h28 help

Answer 1

Ok so this problem uses the 'sin' concept; as in sin, cos, tan. Sound familiar?

Answer 2

Basically, in a right triangle, we can take any angle and we'll know the ratios of the opposite edge and the adjacent edge based on the angle

Answer 3

As a side note, if you didn't already know, a diagram called the 'unit circle' can help as a reference for these kinds of problems. Let me see if I can give you an example.

Answer 4

Here's a link to a wiki page with a diagram you can reference while I explain
https://en.wikipedia.org/wiki/Unit_circle#Circle_group

Answer 5

im not learning that so i dont think we need it

Answer 6

I see. Sorry, I assumed this was trigonometry. In fact, there actually is an easier way to explain this problem that doesn't involve those concepts.

Answer 7

It's geometry its alright

Answer 8

cool

Answer 9

It's all good. This was actually so long ago that I forgot about it. I had to reach wayyyy back to middle school for this one.
You just need to use something called the 30-60-90 rule, which applies to right triangles with angles measuring 30, 60, and 90 degrees.
Does this sound more familiar?

Answer 10

no lol, but maybe it'll work

Answer 11

Ok, I'll break it down. Super simple, I promise.
If we have a right triangle with angles of 30 degrees and 60 degrees, we know what the ratios of the sides will be. So, if we know the length of any of the edges, we can calculate the lengths of all the other edges.
Namely, the length of the shortest edge will be exactly half of the length of the longest edge (the hypotenuse). The length of the middle edge, located between the 30 degree angle and the right angle, will be equal to the length of the shortest edge multiplied by the square root of 3.

Answer 12

You can verify this for yourself with he Pythagorean theorem, a^2 + b^2 = c^2... But I'm getting off topic again.

Answer 13

pythagorean theorem is apart of what I learned

Answer 14

Ok, awesome! We don't need pythagorean theorem for this particular problem, but it's nice to have whenever you're dealing with right triangles.

Answer 15

Back to the problem:
We have two triangles to work with: The triangle made up of the points helicopter-zoo-rightangle; and the triangle made up of points helicopter-library-rightangle. I'll refer to these two by triangle(z) and triangle(l) for simplicity.

Answer 16

ok

Answer 17

In triangle(z), we don't know the length of the hypotenuse or the shorter leg, but we do know the length of the longer leg: 300 times square root of 3.
So, using what we know about the ratios of the edges in a 30-60-90 triangle, how would we calculate the length of the shorter leg?

Answer 18

the length of the shorter leg is half of the longest leg?

Answer 19

My wording was a little jumbled earlier, so I'll restate the rules:
The length of the longer leg is equal to the length of the shorter leg multiplied by square root of 3;
The length of the hypotenuse is equal to the length of the shorter leg times two.

Answer 20

519.61524227066

Answer 21

Oh, gee, you have a calculator, I guess. No worries, but we can simplify things.
Can you tell me what you did to get that number?

Answer 22

\[300\times \sqrt{3}\]

Answer 23

Ok, I see. Let's take a step back from the problem and look at the big question.
At the end of this, we want to know the distance between the zoo and the library. So, it makes sense that we'd need to know the bottom lengths of the two triangles, so that we can take the difference between them. That's where we're trying to get.
So, working backwards from there, we already know one of the lengths is 300 * squareroot(3), which, as you calculated, is about 519.
So, from here, which length would you like to find next?

Answer 24

Zoo to the library

Answer 25

Well, from where we left off, we were trying to find the length of the shorter leg of triangle(z). We know the longer leg of triangle(z) is 300 * squareroot(3). We also know that, for 30-60-90 triangles, the longer leg is equal to the shorter leg multiplied by, well, the square root of 3.

Answer 26

yes

Answer 27

In other words, the shorter leg is equal to the longer leg divided by the square root of 3

Answer 28

And, 300 multiplied by the square root of 3, divided by square root of 3 is...?

Answer 29

519 divided by the square root of 3?

Answer 30

299.7

Answer 31

So, you are correct. The point I'm trying hit home is that if we multiply a number by x, then divide it by x, the number doesn't change. In this case, we can treat square root of 3 as 'x'.
So, 300 * x / x is, as you calculated, 300.

Answer 32

oh

Answer 33

Sorry, I guess that was kind of a roundabout way of explaining things. I'll try to be more straightforward.

Answer 34

So, we're making progress. We know the distance from the zoo to point G (the right angle).
Now, if we can find the distance from the library to point G, we just have to find the difference between those lengths to find the distance between the zoo and library.

Answer 35

How do we find G to library?

Answer 36

I agree, that's the next question we should ask ourselves.
Let's use what we know about 30-60-90 triangles once more.

Answer 37

So, looking at the library triangle, the length that extends from point G to the library is also the longer leg of the 30-60-90 triangle. Just like before, we know the length of the other leg is 300 * sqrt(3). Only this time, we're going from the shorter leg to the longer leg. So, instead of dividing by sqrt(3), we'd do the opposite and multiply by sqrt(3).

Answer 38

(At the risk of sounding patronizing, I'll add a quick reminder that the square root of 3 multiplied by the square root of 3 is... 3. I'm sure you've learned about square roots.)

Answer 39

so 299 multiplied by square root 3

Answer 40

Well, not quite. Remember, 299 (well, really, 300), is the length from the zoo to point G, which we found in our last calculation.

Answer 41

So, in the first, smaller triangle 300 * sqrt(3) was the length of the longer leg. We divided by sqrt(3) to find the length of the shorter leg. This simplified to 300. Would you agree so far?

Answer 42

yes

Answer 43

Alright, so in the second, larger triangle, we're still working with 300*sqrt(3)
But
This time, 300*sqrt(3) is the length of the *shorter* length, and we need to calculate the length of the *longer* length.

Answer 44

So, where in the first case we divided 300*sqrt(3) by sqrt(3), in this case we would multiply 300*sqrt(3) by sqrt(3)

Answer 45

895

Answer 46

Ok, very close. The answer would be 900, and here's why:
sqrt(3) * sqrt(3) = 3
3 * 300 = 900
So,
300 * (sqrt(3) * sqrt(3)) = 300 * 3 = 900

Answer 47

wow awesome

Answer 48

In any case, I'm very glad we've made it this far.
One last step.
We know the distance from the library to point G is 900.
We know the distance from the zoo to point G is 300.
And, as we can see from the diagram, the library, the zoo, and point G are on the same straight line.
So, I'll let you find the answer: What is the distance from the zoo to the library?

Answer 49

600

Answer 50

By George, I think you've got it!
Any clarifications I need to make before we sign off?

Answer 51

No lol, we did it ! yay thanks for all the help gtg bye

Answer 52

Thank you for your patience.
Good night, and take care.