How do you find the other two side of a right triangle ABC, if #∠B=60# and #AB=12# where AB is the hypotenuse?

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Answer 1 · 2014-11-06T11:26:13

#mathbf{30^circ"-"60^circ"-"90^circ}# Triangle

The ratios of three sides of a #30^circ"-"60^circ"-"90^circ# triangle are:

#1:sqrt{3}:2#

Since the posted Triangle ABC is a #30^circ"-"60^circ"-"90^circ# triangle, we have the ratios:

#BC:AC:AB = 1:sqrt{3}:2#

#AB=12 => BC={AB}/2=12/2=6#

#AC=BC cdot sqrt{3}=6sqrt{3}#

Hence, #BC=6# and #AC=6sqrt{3}#.

I hope that this was helpful.