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 $36$ $36$ 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 · 2018-05-15T06:54:40

$a = 72$ $a=72$

$b = 63.35$ $b=63.35$

$\frac{a}{sin [\frac{π}{2}]} = \frac{36}{sin [\frac{π}{6}]}$ $a/[sin[pi/2]]=36/[sin[pi/6]$

$a = sin [\frac{π}{2}] \times \frac{36}{sin [\frac{π}{6}]}$ $a=sin[pi/2] xx 36/[sin[pi/6]$

a=72

$\frac{π}{6} + \frac{π}{2} = \frac{4 π}{6}$ $pi/6+pi/2=(4pi)/6$

so angle B = $\frac{π}{3}$ $pi/3$

$\frac{b}{sin [\frac{π}{3}]} = \frac{36}{sin [\frac{π}{6}]}$ $b/[sin[pi/3]]=36/[sin[pi/6]$

$b = sin [\frac{π}{3}] \times \frac{36}{sin [\frac{π}{6}]}$ $b=sin[pi/3] xx 36/[sin[pi/6]$

$b = 36 \sqrt{3}$ $b=36sqrt3$

$b = 62.35382907$ $b=62.35382907$

A triangle has sides A, B, and C. The angle between sides A and B is π6(pi)/6. If side C has a length of 3636 and the angle between sides B and C is π2( pi)/2, what are the lengths of sides A and B?