A triangle has sides A, B, and C. The angle between sides A and B is $(5pi)/6$ . If side C has a length of $14$ and the angle between sides B and C is $pi/12$ , what are the lengths of sides A and B?

Question

1430 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-18T12:51:56

Lengths of sides $color(brown)(a = b = 7.2469)$

To find the lengths of sides a, b.

Given $hatA = pi/12, hatC = (5pi)/6, c = 14$

Third angle $hat B = pi - pi/12 - (5pi)/6 = pi/12$ by the law of sines.

As $hat B = hat C$ , it’s an isosceles triangle, with sides a, b equal.

$a / sin A = b / sin B = c / sin C$

$a = b = (c * sin A) / sin C = (14 * sin (pi)/12) / sin ((5pi)/6) = color(brown)7.2469$

A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/6(5pi)/6. If side C has a length of 14 14 and the angle between sides B and C is pi/12pi/12, what are the lengths of sides A and B?