A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 5, respectively. The angle between A and C is $(5pi)/8$ and the angle between B and C is $(pi)/12$ . What is the area of the triangle?

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Answer 1 · 2016-12-20T21:00:49

$5.95$ square units

$A_triangle = 1/2ab sin C$

the angle to take as $C$ is the angle sandwiched between the $2$ given sides.

angle sandwiched between A and B = $pi -( 5pi)/8 - pi/12$

$=(24pi)/24 - (15pi)/24 - (2pi)/24$

$=(7pi)/24$

$A_triangle = (3*5)/2 * sin((7pi)/24)$

$= 7.5sin((7pi)/24)$

$=5.95$ square units

(NB: when using $pi$ as a measurement of angles, use the $Rad$ setting on your calculator)

A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 5, respectively. The angle between A and C is (5pi)/8(5pi)/8 and the angle between B and C is (pi)/12 (pi)/12. What is the area of the triangle?