Question

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@zepdrix

Answer 1

Have you learned `Soh Cah Toa` or something similar?
A way to remember the relationships of each trig function.

Answer 2

Yes.

Answer 3

I have labeled the sides in relation to the angle we were given.

Answer 4

We were given the adjacent length, and need to solve for the opposite length.
Which trig function involves `opposite` and `adjacent` ?

Answer 5

We need to find the opposite, don't we? Since we're finding the length, wouldn't it be: Adjacent/Hypotenuse?

Answer 6

So wouldn't it be

55/5

Answer 7

Or, wait. Cos 55* = 5? or something?

Answer 8

So yes you need to use those two pieces of information.
But that's not where we want to put the 55.
We want to apply the trig function to our angle.

Yes you're closer now.

Answer 9

What is the trig function?

Answer 10

\[\Large\bf\sf \cos55^o\quad=\quad \frac{adjacent}{hypotenuse}\]Cosine involves the hyptoenuse. We don't want to use that one.

Answer 11

Soh Cah `Toa`
\[\Large\bf\sf \tan 55^o\quad=\quad \frac{opposite}{adjacent}\]

Answer 12

Wait, comp I thought you knew up to Calculus ;o

Answer 13

The side `adjacent` (next to) our angle, is the 5 length.
We're calling our opposite side a length of x.\[\Large\bf\sf \tan 55^o\quad=\quad \frac{x}{5}\]

Answer 14

Wait wait! If we're trying to find the opposite, then wouldn't we need to find the hypotenuse and adjacent?

Answer 15

No.
You are given the angle value, and the value of the side adjacent to that angle.

Answer 16

I mean, do you understand my logic I am using? If I had a spot on a triangle I wanted to know, then I would find two degrees, then I would know the third degree. You see what I'm doing?

Answer 17

Ah yes I see your logic :)

Answer 18

Triangles are kinda sneaky.
You don't need the other two sides in order to find the third.
You need `two of three` pieces of information to find the rest.

Answer 19

\[\tan {\theta} = \frac{ opp }{ adjacent } ----> \tan 55^o = \frac{ x}{ 5 } \]
x = opposite side to angle = length

Answer 20

So in this case, we're given `angle` and `a side`.
That's enough information to find the rest of the stuff.

Answer 21

Fascinating. So why would I use tan? Could you explain that?

Answer 22

Since we were given these two pieces of information,

Answer 23

we want to use a trig function that involves both of them.

That leaves us with cosine or tangent.
(Sine wouldn't use the 5).

Answer 24

So immediately we're dealing with an angle + adjacent side.
Then we notice that we're trying to find the length of the `opposite side`.

So that's telling us we need to use a trig function which involves the adjacent and opposite sides.

Answer 25

Hmm hard to word this in a nice way lol

Answer 26

Here is something to think about.
You `could` use the cosine function instead.

It would allow you to find the length of the hypotenuse.
From there you can apply the Pythagorean Theorem to find the missing length.
But that's just extra work going that route +_+

Answer 27

I get it. Mind answering a few more? I am trying to understand this material before finals comes up.