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 $\frac{5 π}{8}$ $(5pi)/8$ and the angle between B and C is $\frac{π}{12}$ $(pi)/12$ . What is the area of the triangle?

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Answer 1 · 2016-12-20T21:00:49

$5.95$ $5.95$ square units

$A_{△} = \frac{1}{2} a b sin C$ $A_triangle = 1/2ab sin C$

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

angle sandwiched between A and B = $π - \frac{5 π}{8} - \frac{π}{12}$ $pi -( 5pi)/8 - pi/12$

$= \frac{24 π}{24} - \frac{15 π}{24} - \frac{2 π}{24}$ $=(24pi)/24 - (15pi)/24 - (2pi)/24$

$= \frac{7 π}{24}$ $=(7pi)/24$

$A_{△} = \frac{3 \cdot 5}{2} \cdot sin (\frac{7 π}{24})$ $A_triangle = (3*5)/2 * sin((7pi)/24)$

$= 7.5 sin (\frac{7 π}{24})$ $= 7.5sin((7pi)/24)$

$= 5.95$ $=5.95$ square units

(NB: when using $π$ $pi$ as a measurement of angles, use the $R a d$ $Rad$ 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 5π8(5pi)/8 and the angle between B and C is π12 (pi)/12. What is the area of the triangle?