Question

Trigonometry help.

Answer 1

http://i.imgur.com/HUWhxQ8.png

@austinL

Which formula would be the best to calculate this, and why?

Answer 2

Sometimes, too much information can be given :P

You can either use the angle given or you can just ring up old Pythagoras :P

Which are you more comfortable with?

Answer 3

I'd like to use the angle under the method of SOHCAHTOA. I'm not sure whether to use sin, tan, or cos.

Answer 4

Understood :)

Let me just draw that triangle here. No judging my drawing skillz (or lack thereof haha)

Answer 5

See, when you have right triangles, usually, one angle and one side is enough to determine every other part of the triangle. So... you have one unknown, x, and how is that related to your angle?

Is it the the hypotenuse? Is it opposite your angle, or perhaps adjacent?

Which? :)

Answer 6

That is the question, I'd say x is my Opposite Side?

Answer 7

You'd say? :)
I demand confidence :P

Are you SURE that x is OPPOSITE your given 60-degree angle? :D

Answer 8

100 and 2.157 percent positive.

Answer 9

That's better.
And you're right, x IS opposite of the 60 degree angle.
Now we make use of a given side.

(normally, I'd say we make use of THE given side, but as there are two of them...)

Pick one. It doesn't matter which, as normally, there should only be one given side.

Answer 10

The adjacent.

Answer 11

Good. The adjacent side measures...?

Answer 12

5 in the example image.

Answer 13

Okay.
So we have an unknown OPPOSITE side (x)
and we have a known ADJACENT side (5)
Which of sin, cos, and tan, RELATE OPPOSITE AND ADJACENT?

^^

Answer 14

tan, Yes?

Answer 15

Yup.

tan(60) = opposite / adjacent
In your case, this happens to mean
tan(60) = x / 5.

If I say you're more than capable of doing the rest, would I be correct? ^^

Answer 16

Yep. x = about 8.66.

Answer 17

Well, yeah :)
Unlike our mutual friend Austin, however, I'm a maths student, I generally prefer leaving it in radical form
\[\Large x = 5\sqrt3\]
But if that suits your purposes, then you're right :D

Answer 18

Got it, thanks! By the way, why did we do x/5 instead of x/10, isn't 10 the adjacent?

Answer 19

Errr, perhaps I'm confusing the example with my actual question, Haha.

Answer 20

I like your inquisitive thought process, it's certainly conducive to a good logical student of mathematics :P

By all rights, the 10-long side IS adjacent to the 60-degree angle, but in our case it also happens to be the HYPOTENUSE, and so must be considered as such ^^

Answer 21

So I would use x/5 for my provided example image as well then. Yes?

Answer 22

Yes. If you're up to it, let's do an exercise. Let's forget the 5-long side and use the 10-long one instead, you up for it?

If done correctly, we SHOULD get the correct answer...

Answer 23

Alright, let's do it.

Answer 24

Okay, the 10-long side, as I previously mentioned, is the HYPOTENUSE.

Let's do that process again:
We have an unknown OPPOSITE side
and we have a known HYPOTENUSE

Which of sin, cos, and tan, relate OPPOSITE and HYPOTENUSE?

^^

Answer 25

sin, Yes?

Answer 26

That is correct :)

sin(60) = opposite / hypotenuse
in this case
sin(60) = x / 10

I'm sure you can work this out.
Let me know when you're done ^^

Answer 27

I know you already know the answer from when we did it last time, but try working it out from this way, at least to convince yourself that it won't matter which way you pick :D

Answer 28

Alright awesome! I am still somewhat curious (probably due to my ignorance) why 10 is the hypotenuse, and 5 is the adjacent.

Answer 29

Then let me enlighten you (LOL)
In a right triangle, the hypotenuse is the LONGEST side.

That's not really saying much, so let me put it this way:
All angles, even the RIGHT angle in the right triangle, have opposite sides.

The side that happens to lie opposite to the RIGHT angle IS the hypotenuse.

All clear now? ^^