John is filling a bathtub that is 18 inches deep. He notices that it takes two minutes to fill the tub with three inches of wate
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Answer:
Step-by-step explanation:
We want to find a formula for <em>s</em> in terms of <em>a, b, </em>and cos(x).
Let the point where <em>s</em> intersects AB be D.
Notice that <em>s</em> bisects ∠C. Then by the Angle Bisector Theorem:
We can find BD using the Law of Cosines:
Likewise:
From the first equation, cross-multiply:
And square both sides:
Substitute:
Distribute:
Simplify:
Divide both sides by <em>s </em>(<em>s</em> ≠ 0):
Isolate <em>s: </em>
Factor:
Therefore:
Factor:
Simplify. Therefore: