Question

Max observes the zoo and the library from a helicopter flying at a height of 400 times square root of 3 feet above the ground, as shown below:

Here are the choices:
A) 800 Feet
B) 600 Feet
C) 200 Feet
D) 400 Feet

The picture for this problem will be shown below:

Answer 1

what are you trying to find here ?

Answer 2

Oh, sorry, I forgot to put that in haha.

What is the distance between the zoo and the library?

Answer 3

Hello? @ganeshie8

Answer 4

\[ZL=GL-GZ\]
Use \[\triangle GHZ\]
to find GZ
and
\[\triangle GHL\]
to find GL

Answer 5

the tangent function will be your help here

Answer 6

Okay, I'm understanding so far. How would I write that formula out though? Well, not just tell me but, explain how I'd work it out.

Answer 7

In
\[\triangle GHZ\]
\[\tan(60)=\frac{GH}{GZ}\]
see the point now?

Answer 8

Okay, so basically there are 2 problems here? But yes, I'm understanding so far since those are the opposite and adjacent sides.

Answer 9

In a sense, yes, you will have to use 2 separate triangles to find 2 values

Answer 10

for you reference, I shall provide the values of tan30 and tan60
\[\tan(30)=\frac{1}{\sqrt{3}}\]
\[\tan(60)=\sqrt{3}\]

Answer 11

Why is tan(30) = 1/3? and tan(60) = 3?

Answer 12

Well, it's a function, functions take in variables (angles in this case) and return some value depending on the value of the variable
and it's 1/sqrt(3) and sqrt(3)
For example consider
\[x^2+7x\]
What you are asking is something like why will x=1 give us the answer as 8?

Answer 13

One moment please. :)

Answer 14

Sure

Answer 15

Okay, I'm back. I'm still a bit confused. I understand functions need variables. But are we using sqrt because of the 400sqrt{3} ??

Answer 16

Ok let's take my same example
\[x^2+7x\]
When x=1, we get
answer as 8
Similarly consider
\[\tan(x)\]
when
\[x=60\]
degrees
we get the answer as
\[\sqrt{3}\]
It's one of those things you need to remember, I can't help much if you ask "why" is this so?

Answer 17

Infact you are given the height of the tower as PRECISELY as 400sqrt{3} so that your calculations would be easier

Answer 18

sorry height of helicopter

Answer 19

Ok, now I understand what you're trying to stay, just for the sake of curiosity, let me tell you that tan(x) can represented as an infinite series of x,
\[\tan(x)=x+\frac{2x^3}{3!}+\frac{16x^5}{5!}+\frac{272x^7}{7!}+....\]
This is mclaurin series for tan(x), basically mclaurin series are a way of representing functions as an infinite polynomial
where x is in radians
let's convert 60 to radians
\[60 \times \frac{\pi}{180}=\frac{\pi}{3}\]
Now when you put x=pi/3, for each term you add, your value will get closer and closer to \[\sqrt{3}\]
Now don't ask where I pulled that series out from, it's totally out of bounds fornow, I did this for the sake of visualization, and don't go around wasting time putting pi/3 in all those terms, you will get the answer as sqrt{3}
the ! means
\[3!=3 \times 2 \times 1\]
\[5!=5 \times 4 \times 3 \times 2 \times 1\]
It's a way of writing product from that number to 1

Answer 20

I'm sorry if I can't find an easier way to tell you, but for now just remember that
\[\tan(60)=\sqrt{3}\]
and
\[\tan(30)=\frac{1}{\sqrt{3}}\]

Answer 21

It's okay, I don't want you to try and help me understand for too long. I'll ask my teacher about it as well and look over my notes again, but let's just continue.

Answer 22

You don't need to worry about asking my help for long, If I was busy I wouldn't come to the website in the first place, right?