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
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
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/
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
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