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In right triangle ABC with right angle C, AC=9 and the measure of angle B=30 degree. Find the length of AB.

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[tex]From\ triangle\ with\ angles: 30^{\circ},60^{\circ},90^{\circ}\\\ |AB|=a\sqrt{3}\\ |AC|=a=9\\\\ |AB|=9\sqrt{3}\\\\ Length\ of\ |AB|\ is\ equal\ to\ 9\sqrt{3}. [/tex]
Since you know angle B and length of ac, you can use the Sin ratio to determine the length of ab. Set up as Sin30 = 9/x. As sin= opp/hyp and x=unknown length.
Then cross multiply and divide. move x over to sin30, then move sin30 under 9.
So now you have x= 9/Sin30. enter in calculator, but make sure you are in degree mode!!!

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