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#