A triangle has sides A,B, and C. If the angle between sides A and B is #(3pi)/8#, the angle between sides B and C is #pi/6#, and the length of B is 10, what is the area of the triangle?

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Answer 1 · 2018-06-05T11:17:09

#"Area " ~~ color(red)(23.3 " sq units"#

#3/8pi+pi/6=13/24pi# so the third angle is #11/24pi#

using the sine rule

#10/[sin(11/24pi)]=c/[sin(3/8pi)]#

#c ~~color(red)( 9.32#

area=#1/2#absinC

area=#1/2 xx 10 xx color(red)(9.32) xx sin (pi/6)#

#"Area = (1/2) * 10 * color(red)(9.32) * (1/2)

#"Area " = (10/4) * 9.32 = 2.5 * 9.32 ~~ color(red)(23.3 " sq units"#