Anyone know anything about sine rules?

Question

I have to do them next semester and It's only wise to put in some work during the holidays. Anyhows, like, is it as simple as SineA/a= SineB/b= SineC/c? With the / sign denoting division. Is that all we need to know? It couldn't be that simple, could it?

Hi Bob, Um well If I've got it right then the sine of 120degres is simply 0.8660254038. It should be, from memory, just like finding a sine in trigonometry. Is that right?

Answer 1

Almost. You'll also need to learn how to resolve some ambiguities. For example:

What's the sine of 60 degrees?

What's the sine of 120 degrees?

Answer 2

What you're referring to is generally called the "Law of Sines," and it's a relationship that applies to the sides and angles of any triangle. (We're assuming that A, B, and C are the measures of the angles, and a, b, and c are the lengths of the sides, and that A is the angle opposite side a, etc.)

There's also the Law of Cosines, which is sort of a generalized version of the Pythagorean Theorem; it applies to any triangle, not just a right triangle:

c² = a² + b² - 2ab cos C

(Of course, since how we notate our sides -- which ones we call a, b, and c -- is complete arbitrary, there are two perfectly equivalent ways to write the Law of Cosines:
b² = a² + c² - 2ac cos B
a² = b² + c² - 2bc cos A
but the first way is the way you'll typically see it.)

There's also a lesser used Law of Tangents:

(a - b)/(a + b) = tan [(A-B)/2] / tan [(A+B)/2]

There are other trig identities, too, which you'll find at the link below, but those are the three that are commonly used to "solve triangles."

Hope that helps!

Answer 3

The weblink recommended by Sherman81 is a very good resource. It contains special angles, all the sine, cosine rules and half-angle (take the sqrt of the cos^x and sin^x formulas) rules.

I was in school over 30 years ago and we had no calculators so instead we used sine/cosine tables and linear interpolation for non-special angles.

My advice is that you learn to derive all these formulae - this way you will have less to remember. You can search for derivations by typing "proof sine formula" in some search engine. The proofs are very easy. Next, you should go to tutorial websites that have drill exercises - actual word problems involving elevation, distance, etc.

Answer 4

these rules are from the chapter properties of triangle basically all of them is equal to R(radius) of incircle A,B,C angles of triangle and a,b,c lengths of triangle

Answer 5

basically it is that simple only just think of any right triangle
then your equation would feet into any where

Answer 6

if you dont believe your senses then derive another one hehe im on 600 pts

Answer 7

this should help out

http://www.math.com/tables/trig/identities.htm