A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $pi/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 18, 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 $\frac{π}{6}$ $pi/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 18, what is the area of the triangle?

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Answer 1 · 2017-08-12T11:56:01

Area of the triangle is $29.65$ $29.65$ sq.unit.

Explanation:

The angle between sides A and B is $∠ c = \frac{π}{6} = \frac{180}{6} = 30^{0}$ $/_c = pi/6 =180/6=30^0$

The angle between sides B and C is $∠ a = \frac{π}{12} = \frac{180}{12} = 15^{0}$ $/_a = pi/12 =180/12=15^0$

The angle between sides C and A is

$∠ b = 180 - (30 + 15) = 135^{0}, B = 18$ $/_b = 180-(30+15)=135^0 , B=18$ Applying sine law we get

$\frac{A}{sin a} = \frac{B}{sin b} or A = B \cdot \frac{sin a}{sin b} = 18 \cdot \frac{sin 15}{sin 135} \approx 6.59$ $A/sina = B/sinb or A= B*sina/sinb= 18 *sin15/sin135 ~~ 6.59$

Now we have side $A = 6.59, B = 18$ $A = 6.59 , B=18$ and their included angle

$∠ c = 30^{0}$ $/_c = 30^0$ . Area of the triangle is $A_{t} = \frac{A \cdot B \cdot sin c}{2}$ $A_t=(A*B*sinc)/2$ or

$A_{t} = \frac{6.59 \cdot 18 \cdot sin 30}{2} \approx 29.65$ $A_t=(6.59*18*sin30)/2 ~~ 29.65$ sq.unit [Ans]

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $pi/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 18, 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 pi/6π6pi/6 and the angle between sides B and C is pi/12π12pi/12. If side B has a length of 18, 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 $\frac{π}{6}$ $pi/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 18, what is the area of the triangle?