Question

ok obiviously im trying to figure out all types of questions that im a little iffy on before I take my trig finale. so I have a word problem I don't seem to understand:
two radar stations are 50 miles apart. Both are tracking the same plane. at the moment, the angle between station 1 and the plane is 73 degrees, and the angle between station 2 and the plane is 46 degrees how far is the plane from station 2.

Answer 1

I think you can use law of sin for this. where
\[\frac{ a }{ \sin A } = \frac{ b }{ \sin B } = \frac{ c }{ \sin C }\]

Answer 2

Oops, I swapped c and C, C is the angle, c is the length.
in your case you have A and B, so you can find C.

Answer 3

so \[A \div \sin(73)= B \div \sin(46)=C \div \sin(x) \]
where do I go from there

Answer 4

So x is 180 - 73 - 46 = 61 so you have the ratio is 50/sin(61) = 57.16.
Then you should be able to find the remaining 2 sides

Answer 5

ok so if I am using angle B
in my case it is equal to 46 degrees. and trying to find length a what side would each other length be so I can determine what I use. because I think hypotenuse would be b and adjacent would be C so that would be 50 and then solve for the opposite, but im confused on how I would figure out where to put each side length. in other words. if I wanted to use sin that equals O/H, would that work to solve for the side im looking for or would that solve for the other side then I would need to use coswhich is A/h because then I would only have one more side I was looking for?

Answer 6

sorry, got interrupted
\[\frac{ 50 }{ \sin(61) } = 57.16\]
and you want to find length a, so you need sin(A)
\[\frac{ a }{ \sin(A) } = 57.16 => a = 57.16 * \sin(A)\]
Remember to set you calculator to degree