How to calculate law of sines?

You only know the angle α and sides a and c; Angle α is acute ( α < 90° ); a is shorter than c ( a < c ); a is longer than the altitude h from angle β, where h = c * sin (α) (or a > c * sin (α) ).

https://www.omnicalculator.com/math/law-of-sines

What are the rules of Sine and cosine?

The sine rule can be used to find an angle from 3 sides and an angle, or a side from 3 angles and a side. The cosine rule can find a side from 2 sides and the included angle, or an angle from 3 sides.

https://www.mathcentre.ac.uk/resources/Engineering maths first aid kit/latexsource and diagrams/4_6.pdf

How can one prove the law of cosines?

Proof of the Law of Cosines The Law of Cosines states that for any triangle ABC, with sides a,b,c For more see Law of Cosines. In the right triangle BCD, from the definition of cosine: or, Subtracting this from the side b, we see that In the triangle BCD, from the definition of sine: or In the triangle ADB, applying the Pythagorean Theorem

https://www.themathdoctors.org/proving-the-law-of-cosines/

When to use the law of sines?

We can use the Law of Sines again, this time including side b and angle B: a/sin (A) = b/sin (B) 6/sin (45) = b/sin (75) 6sin (75) = bsin (45) [cross multiply to eliminate fractions] 6 (0.9659) = b√2/2 [approximate value for sine of 75 degrees] 6 (0.9659)*2/√2 = b 8.196 = b

https://www.math.net/law-of-sines