A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $pi/6$ . If side C has a length of $3$ $3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $pi/6$ . If side C has a length of $3$ $3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?

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Answer 1 · 2017-10-14T16:50:06

$A = \frac{3}{2} (\sqrt{6} - \sqrt{2}) ≅ 1.55$ $A=3/2(sqrt6-sqrt2)~=1.55$

Explanation:

The Euler theorem (or sine theorem) states that:

$\frac{A}{sin ˆ B C} = \frac{B}{sin ˆ A C} = \frac{C}{sin ˆ A B}$ $A/sin hat(BC)=B/sin hat(AC)=C/sin hat(AB)$

Let's find A by using the relation:

$\frac{A}{sin ˆ B C} = \frac{C}{sin ˆ A B}$ $A/sin hat(BC)=C/sin hat(AB)$

from which:

$A = \frac{C \cdot sin ˆ B C}{sin ˆ A B} = \frac{3 \cdot sin (\frac{π}{12})}{sin (\frac{π}{6})}$ $A=(C*sin hat(BC))/sin hat(AB)=(3*sin(pi/12))/sin (pi/6)$

$A = \frac{3 \cdot \frac{1}{4} (\sqrt{6} - \sqrt{2})}{\frac{1}{2}} = \frac{3}{2} (\sqrt{6} - \sqrt{2}) ≅ 1.55$ $A=(3*1/4(sqrt6-sqrt2))/(1/2)=3/2(sqrt6-sqrt2)~=1.55$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $pi/6$ . If side C has a length of $3$ $3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?

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A triangle has sides A, B, and C. The angle between sides A and B is π6pi/6. If side C has a length of 33 and the angle between sides B and C is π12pi/12, what is the length of side A?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $pi/6$ . If side C has a length of $3$ $3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?