A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{12}$ $pi/12$ , the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , and the length of B is 5, what is the area of the triangle?

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{12}$ $pi/12$ , the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , and the length of B is 5, what is the area of the triangle?

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Answer 1 · 2017-10-14T04:06:00

Area of triangle = 3.0026

Explanation:

$∠ A = \frac{π}{12}, ∠ C = \frac{π}{12}, ∠ B = \frac{5 π}{6}$ $/_A=pi/12, /_C=pi/12, /_B=(5pi)/6$
Side $B = 5$ $B=5$
We know, $\frac{A}{sin A} = \frac{B}{sin B} = \frac{C}{sin C}$ $A/sin A=B/sin B=C/sin C$
$\frac{A}{sin (\frac{π}{12})} = \frac{5}{sin (\frac{5 π}{6})} = \frac{C}{sin (\frac{π}{12})}$ $A/sin (pi/12)=5/sin ((5pi)/6)=C/sin (pi/12)$
$A = \frac{5 \cdot \frac{sin (π)}{12}}{sin (\frac{5 π}{6})} \approx 2.5881$ $A=(5*sin (pi)/12)/sin ((5pi)/6)~~2.5881$
As $∠ A = ∠ C, ∠ C \approx 2.5881$ $/_A=/_C, /_C~~2.5881$

$s = \frac{A + B + C}{2} = \frac{5 + 2.5881 + 2.5881}{2} = 5.0881$ $s=(A+B+C)/2=(5+2.5881+2.5881)/2=5.0881$
$s - A = s - C = 5.0881 - 2.5881 = 2.5$ $s-A=s-C=5.0881-2.5881=2.5$
$s - B = 5.0881 - 5 = 0.0881$ $s-B=5.0881-5=0.0881$

Area of triangle = $\sqrt{s \cdot (s - A) (s - B) (s - C)}$ $sqrt(s*(s-A)(s-B)(s-C))$
$= \sqrt{5.0881 \cdot 2.5881 \cdot 0.0881 \cdot 2.5881} = \approx 3.0026$ $=sqrt(5.0881*2.5881*0.0881*2.5881)=~~3.0026$

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{12}$ $pi/12$ , the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , and the length of B is 5, what is the area of the triangle?

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A triangle has sides A,B, and C. If the angle between sides A and B is π12pi/12, the angle between sides B and C is π12pi/12, and the length of B is 5, what is the area of the triangle?

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{12}$ $pi/12$ , the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , and the length of B is 5, what is the area of the triangle?