A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/6#. If side C has a length of #1 # and the angle between sides B and C is #( pi)/2#, what are the lengths of sides A and B?

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Answer 1 · 2016-02-21T04:00:59

Lengths of sides: #a=2# and #b=sqrt3#

You can solve this by the Right Triangle formulas because angle #A=pi/2=90^@# and angle #C=pi/6=30^@#

with side #c=1#

#sin C=c/a#

#sin (pi/6)=1/a#

#a=1/sin (pi/6)=1/(1/2)=2#

#Tan C=c/b#

#tan (pi/6)=1/b#

#b=1/tan (pi/6)=1/(1/sqrt3)=sqrt3#

This is a special Right Triangle :

The Angles are #A=90^@#, #C=30^@#, #B=60^@#

The sides are #a=2#, #c=1#, #b=sqrt3#

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