A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{3}$ $pi/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 5, 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 $\frac{π}{3}$ $pi/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 5, what is the area of the triangle?

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Answer 1 · 2016-05-19T09:06:56

Area of triangle is $2.90$ $2.90$

Explanation:

The third angle opposite sides $A$ $A$ and $C$ $C$ is

$π - \frac{π}{3} - \frac{π}{12} = (12 - 4 - 1) \frac{π}{12} = 5 \frac{π}{12}$ $pi-pi/3-pi/12=(12-4-1)pi/12=5pi/12$ and it has side $B = 5$ $B=5$ opposite it.

As side $A$ $A$ has angle opposite it $\frac{π}{12}$ $pi/12$ , using sine formula, we get

$\frac{A}{sin (\frac{π}{12})} = \frac{B}{sin (\frac{5 π}{12})}$ $A/sin(pi/12)=B/sin((5pi)/12)$ or

$A = B \times \frac{sin (\frac{π}{12})}{sin (\frac{5 π}{12})} = 5 \times \frac{0.2588}{0.9659} = 1.34$ $A=Bxxsin(pi/12)/sin((5pi)/12)=5xx0.2588/0.9659=1.34$

Hence area of triangle is $\frac{1}{2} \times 5 \times 1.34 \times sin (\frac{π}{3})$ $1/2xx5xx1.34xxsin(pi/3)$

= $\frac{1}{2} \times 5 \times 1.34 \times 0.866 = 2.90$ $1/2xx5xx1.34xx0.866=2.90$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{3}$ $pi/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 5, what is the area of the triangle?

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Explanation:

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A triangle has sides A, B, and C. The angle between sides A and B is pi/3π3pi/3 and the angle between sides B and C is pi/12π12pi/12. If side B has a length of 5, what is the area of the triangle?

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Explanation:

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{3}$ $pi/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 5, what is the area of the triangle?