A triangle has sides A, B, and C. The angle between sides A and B is $(3pi)/4$ and the angle between sides B and C is $pi/12$ . If side B has a length of 4, what is the area of the triangle?

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A triangle has sides A, B, and C. The angle between sides A and B is $(3pi)/4$ and the angle between sides B and C is $pi/12$ . If side B has a length of 4, what is the area of the triangle?

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Answer 1 · 2016-09-03T14:15:42

$S=4sqrt(4-sqrt6)$

Explanation:

The angle between A and C is $pi-3pi/4-pi/12=pi/6$
Acording theorem of sin length C: $C/sin(3pi/4)=4/sin(pi/6)$
$C=4sqrt2$
Area of the triangle: $S=BCsin(pi/12)/2$
$sin(pi/12)=sqrt((1-cos(pi/6))/2)$
$sin(pi/12)=sqrt(2-sqrt3)/2$

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A triangle has sides A, B, and C. The angle between sides A and B is $(3pi)/4$ and the angle between sides B and C is $pi/12$ . If side B has a length of 4, what is the area of the triangle?

1 Answer

Explanation:

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A triangle has sides A, B, and C. The angle between sides A and B is (3pi)/4(3pi)/4 and the angle between sides B and C is pi/12pi/12. If side B has a length of 4, what is the area of the triangle?

1 Answer

Explanation:

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A triangle has sides A, B, and C. The angle between sides A and B is $(3pi)/4$ and the angle between sides B and C is $pi/12$ . If side B has a length of 4, what is the area of the triangle?