Law of Sines

Draw a right triangle on a rectangular coordinate system. Label the origin A and the other vertex of the base B. Label the upper vertex C(x,y).

sin A = y/b
y = b sin A

Now draw the same triangle on a rectangular coordinate system, interchanging the vertices at the base. Now the origin is B and the other vertex is A. The upper vertex is still C(x,y).

sin B = y/a
y = a sin B

Since y is the same value in both triangles,

b sin A = a sin B
b sin A = a sin B (Divide both sides by ab)

ab ab

sin A = sin B (Reduce)

a b

Similarly, sin A = sin B = sin C

a b c

Problems

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