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)

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

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