A triangle has sides A, B, and C. The angle between sides A and B is $(7pi)/12$ and the angle between sides B and C is $pi/12$ . If side B has a length of 12, 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 $(7pi)/12$ and the angle between sides B and C is $pi/12$ . If side B has a length of 12, what is the area of the triangle?

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Answer 1 · 2017-05-19T16:00:46

$A=24.053$ $units^2$

Explanation:

$Acolor(white)(00)color(black)(pi/12)color(white)(0000000)acolor(white)(00)color(white)(0)$

$Bcolor(white)(00)color(white)(pi/1 3)color(white)(0000000)bcolor(white)(00)color(black)(12)$

$Ccolor(white)(00)color(black)((7pi)/12)color(white)(0000000)c color(white)(00)color(white)(0)$

Let's find the remaining angle, $B$ :

$pi-pi/12-(7pi)/12$ leaves us with $pi/3$

$Acolor(white)(00)color(black)(pi/12)color(white)(0000000)acolor(white)(00)color(white)(0)$

$Bcolor(white)(00)color(black)(pi/3)color(white)(.)color(white)(0000000)bcolor(white)(00)color(black)(12)$

$Ccolor(white)(00)color(black)((7pi)/12)color(white)(0000000)c color(white)(00)color(white)(0)$

Now we should use law of sines

$(sin(pi/3))/12=(sin(pi/12))/a$

$a~~3.59$

$(sin(pi/3))/12=(sin((7pi)/12))/c$

$c~~13.4$

Now, to find the area, we use the equation $A=(hxxb)/2$ , where $h$ is the height.

$color(white)(a)color(white)(- - - - - - - - - -)color(black)(/)color(black)(|)$
$color(white)(a)color(white)(- - - - - - - - -)color(black)(/)color(white)(-)color(black)(|)$
$color(white)(a)color(white)(- - - - - - - -)color(black)(/)color(white)(- - .)color(black)(|)$
$color(white)(a)color(white)(- - - - - - -)color(black)(/)color(white)(- - -0)color(black)(|)$
$color(white)(- - - -)color(black)(a)color(white)(00000)color(black)(/)color(white)(- - - -0)color(black)(|)color(black)(h)$
$color(white)(a)color(white)(- - - - -)color(black)(/)color(white)(- - - - -0)color(black)(|)$
$color(white)(a)color(white)(- - - -)color(black)(/)color(white)(- - - - - -0)color(black)(|)$
$color(white)(a)color(white)(- - -)color(black)(/)color(white)(- - - - - - -0)color(black)(|)$
$color(white)(a)color(white)(- -)color(black)(/)color(white)(- - - - - - - -0)color(black)(|)$
$color(white)(-)color(black)(/)color(black)(..)color(black)(B)color(black)(........................................)$

$a=3.59$ , and the angle $B$ is $pi/3$ . We need to find the remaining length, $h$ .

$sin(pi/3)=h/(3.59)$

$sin(pi/3)xx3.59=h$

$h=3.11$

Now we can find the area:

$A=(hxxb)/2$

$A=(3.59xx13.4)/2$

$A=24.053$ $units^2$

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A triangle has sides A, B, and C. The angle between sides A and B is $(7pi)/12$ and the angle between sides B and C is $pi/12$ . If side B has a length of 12, 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 (7pi)/12(7pi)/12 and the angle between sides B and C is pi/12pi/12. If side B has a length of 12, 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 $(7pi)/12$ and the angle between sides B and C is $pi/12$ . If side B has a length of 12, what is the area of the triangle?