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 $23$ and the angle between sides B and C is $( 5 pi)/8$ , what are the lengths of sides A and B?

Question

1772 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-24T04:24:29

Lengths of sides $color(brown)(a = 42.5, b = 28$

$hat A = (5pi)/8, hat C = pi/6, c = 23$

To find $a, b$

As per Law of Sines,

$a = (c * sin A) / sin C, b = (c * sin B) / sin C$

$hat B = pi - (5pi)/8 - pi/6 = (5pi)/24$

$a = (23 * sin ((5pi)/8)) / sin (pi/6) = 42.5$

$b = (23 * sin (5pi/24) )/ sin (pi/6) = 28$

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 23 23 and the angle between sides B and C is ( 5 pi)/8( 5 pi)/8, what are the lengths of sides A and B?