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 $a=2$ , $c=1$ , $b=sqrt3$

have a nice day

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