Question

Could I find the two missing angle measures if I know some of the side lengths of a right triangle?

Answer 1

Is it possible to find the two missing angle measures using sin/cos/tan?

Answer 2

if you know what exactly? two sides and one angle?

Answer 3

Two sides and the 90 degree angle, presumably.

Answer 4

yes

Answer 5

actually you don't need a 90 degree angle
two angles and one side will do it, for the most part

Answer 6

But what if we only have the 90 degree angle and 2 sides? How would I find the 2 angles from having those numbers? O.o

Answer 7

in this example
\[\tan(\theta)=\frac{b}{a}\] so
\[\theta =\tan^{-1}(\frac{b}{a})\]

Answer 8

So would I input the (b/a) in my calculator as a fraction or how would I solve that?

Answer 9

@BangkokGarrett Would you be able to help on this one?

Answer 10

Your calculator should have an inverse tangent button
It should look like this
\[\tan ^{-1}\]
calculate b/a
then find the inverse tangent of whatever you get for b/a

Answer 11

Alright so:
1) B/A
2) Calculate the answer of B/A using tan-1

Answer 12

depends on the calculator
usually it is "shift" 'tan"

Answer 13

if you have a specific example, we could do it

Answer 14

the "inverse tangent" of b/a. It will give you the angle.

Answer 15

Here I'll make a specific one - one sec. Thanks for the help btw, I really appreciate it, seeing as I have no idea what I was doing prior to this.

Answer 16

Using this as an example (assuming it's valid) I'll try to give it a go.

Answer 17

1) tan(x) = 25/10
2) 25/10 = 2.5
3) tan-1 + 2.5 = 68.20
4) x = 68.20

Answer 18

@satellite73 @BangkokGarrett

Okay so there's my attempt.

Answer 19

ok so \(\tan(x)=2.5\) and therefore \(x=\tan^{-1}(2.5)\)

Answer 20

about \(68.2\) degrees
http://www.wolframalpha.com/input/?i=arctan%282.5%29

Answer 21

So I did it somewhat right?

Answer 22

oops scratch that, i didn't look carefully
yes you got it !

Answer 23

Oh I didn't mean that I added tan-1 and 2.5, I was just showing that I found the inverse of tan or whatever of it. I don't know how to write it out properly lol

Answer 24

yeah you are right
this line "tan-1 + 2.5 = 68.20" confused me, but you are right

Answer 25

if you have other sides, you have to use other trig functions

Answer 26

here \(\sin(x)=\frac{7}{10}=.7\) and so
\[x=\sin^{-1}(.7)\]

Answer 27

Awesome :D I'm glad I'm finally understanding this stuff!

So to answer my original question (Could I find the two missing angle measures if I know some of the side lengths of a right triangle?), now that I've found one angle, I could simply find the other by using simple addition:

90 and 68.2 are known angles, so that makes 21.8 the last angle?

Answer 28

yes

Answer 29

and also you know the third side by pythagoras, so you know all angles and all sides

Answer 30

Woo! I'm gonna work through an example real quick and show my work, and I'll post it and get your thoughts, if that's alright.

Answer 31

ok , of course

Answer 32

you back?

Answer 33

Yep sorry, had to edit it.

Answer 34

looks pretty damn good to me, although as you pointed out before, you didn't need to use the inverse tangent twice

Answer 35

you could have subtracted 26.6 from 90 to get 63.4 right?

Answer 36

Yeah that's true enough haha, wish I would've done that to save some time. Oh well, at least I understand it now. Thanks a ton for all your help!

Answer 37

yw
let me give you a small word of advice

Answer 38

later you will be solving these triangles with out a 90 degree angle
two things you need to do
1) draw an accurate triangle
2) it is best to solve for the largest angle first

Answer 39

but it looks like you got this, so good work!

Answer 40

Oh alright, good to know! I really appreciate you taking the time to explain this all to me. Pretty dire situation for me concerning my geo class, so I'm really glad I finally get all this BS.