Using the given information in the diagram, we have proven that sin(B)/b = sin(C)/c
Proving the Sine rule
From the question, we are to prove that sin(B)/b=sin(C)/c
Consider the right triangle with sides a, c, and h
Using SOH CAH TOA, we can write that
sin(B) = h/c
∴ h = c × sin(B) --------- (1)
Also,
Consider the other right triangle
Using SOH CAH TOA, we can write that
sin(C) = h/b
∴ h = b × sin(C) ---------- (2)
Equate equations (1) and (2)
That is,
c × sin(B) = b × sin(C)
This can then be expressed as
sin(B)/b = sin(C)/c
Hence, the given expression is proven as shown above
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