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

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

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Answer 1 · 2016-02-21T04:00:59

Lengths of sides: $a = 2$ $a=2$ and $b = \sqrt{3}$ $b=sqrt3$

Explanation:

You can solve this by the Right Triangle formulas because angle $A = \frac{π}{2} = 90^{\circ}$ $A=pi/2=90^@$ and angle $C = \frac{π}{6} = 30^{\circ}$ $C=pi/6=30^@$

with side $c = 1$ $c=1$

$sin C = \frac{c}{a}$ $sin C=c/a$

$sin (\frac{π}{6}) = \frac{1}{a}$ $sin (pi/6)=1/a$

$a = \frac{1}{sin (\frac{π}{6})} = \frac{1}{\frac{1}{2}} = 2$ $a=1/sin (pi/6)=1/(1/2)=2$

$tan C = \frac{c}{b}$ $Tan C=c/b$

$tan (\frac{π}{6}) = \frac{1}{b}$ $tan (pi/6)=1/b$

$b = \frac{1}{tan (\frac{π}{6})} = \frac{1}{\frac{1}{\sqrt{3}}} = \sqrt{3}$ $b=1/tan (pi/6)=1/(1/sqrt3)=sqrt3$

This is a special Right Triangle :

The Angles are $A = 90^{\circ}$ $A=90^@$ , $C = 30^{\circ}$ $C=30^@$ , $B = 60^{\circ}$ $B=60^@$

The sides are $a = 2$ $a=2$ , $c = 1$ $c=1$ , $b = \sqrt{3}$ $b=sqrt3$

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

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