Super quick trig question

Projeck

I have the right answer, just wondering why it's correct

So, I'm supposed to solve this triangle using the law of sines and law of cosines
given A = 50° b = 15 and c = 30

so I plug that into the cos formula :
a^2 = 900 + 225 - 2 (450) cos50° -> some algebra -> a = ~23.38


with that, I go ahead and use the sin formula to find C
23.377 / sin 50° = 30 / sin C -> C = ~79.44°

Then I can find B by subtracting from 180°, and B = ~50.56°

but, that's wrong, (I can check in the back of the book, side a is correct, though) and if I find B and subtract from 180, I get the correct angles

why? (sorry, my teacher is terrible and doesn't explain things)

edit: the correct angles are B = ~29.44° and C = ~100.56°

travathian

Not trying to be a dick, but are you plugging everything into the calculator correctly? Almost all my errors from college algebra thru calc were due to missing something when I went from paper to keypresses or from silly algebra mistakes when I setup the problem.

Projeck

Yeah, I've double checked everything three times now

Awk

are you in degrees or radians mode?

Projeck

degrees

Savant

The problem you are having here is due to finding C using the arcsine, which is the inverse of the sine function. Take a look at the graph here of a simple sine function from 0 to 360 degrees:


Note that this function is not one to one, and that there are multiple angles x which will give the same sin x value. So the inverse of the sine, the arcsine, is in fact not a function.

For your particular problem, your calculator is only giving you one of the possible angles of C which would give you the correct sin C. Note that sin(79.44 degrees) = 0.983063532 = sin(100.56 degrees).

One way this should jump out at you is that if you center yourself at 90 degrees the sine function looks symmetric, and 79.44 and 100.56 degrees have the same absolute distance from 90 degrees. Both angles are potentially valid for being in a triangle, so you'll have to be careful and check yourself when using the inverses of trigonometric functions.

Awk

are you currently in a relationship?

neville

Awk wrote: »

are you currently in a relationship?

seems relevant

Projeck

Thanks savant! Appreciate your help

edit: also, nope