Step-by-step explanation:
It can be misleading to try to think in terms of "multiplying" or "dividing". There is a tendency to try to remember a procedure for solving problems. It can be more useful to remember the relationships involved in a problem.
Once you have an equation based on the relationships, you make use of the rules of algebra to solve it. Sometimes multiplication is involved; sometimes division.
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The trig relations are summarized in the mnemonic SOH CAH TOA. This is intended to remind you ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
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The rules of algebra tell you that these equations can be multiplied by the denominator to eliminate the fractions:
Hypotenuse × Sin = Opposite
Hypotenuse × Cos = Adjacent
Adjacent × Tan = Opposite
Solving any of these equations may involve multiplication, or it may involve division, depending on what you have and what you're solving for.
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In short, remember SOH CAH TOA and the general rules of solving equations. That will tell you whether you need to multiply or divide.