If sides A and B of a triangle have lengths of 8 and 3 respectively, and the angle between them is $(5pi)/8$ , then what is the area of the triangle?

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Answer 1 · 2016-10-02T13:47:23

$11.09$

$"Let's consider the diagram"$

enter image source here

$"I have mentioned"$ $(5pi)/8$ $"as"$ $112.5^circ$

$"We can find the area of a triangle given the length of two sides"$
$"and the angle between them using this formula"$

$color(blue)($ $color(blue)("Area"$ $color(blue)(=1/2*"$ $color(blue)("A"$ $color(blue)(*$ $color(blue)("B"$ $"color(blue)(*sin(c)$

$rarr1/2*8*3*sin(112.5)$

$rarr1/cancel2^1*cancel24^12*sin(112.5)$

$rarr12*sin(112.5)$

$rarr12*0.92$

$color(green)(rArr11.09$

If sides A and B of a triangle have lengths of 8 and 3 respectively, and the angle between them is (5pi)/8(5pi)/8, then what is the area of the triangle?