A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 3, respectively. The angle between A and C is $\frac{13 π}{24}$ $(13pi)/24$ and the angle between B and C is $\frac{3 π}{8}$ $(3pi)/8$ . What is the area of the triangle?

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A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 3, respectively. The angle between A and C is $\frac{13 π}{24}$ $(13pi)/24$ and the angle between B and C is $\frac{3 π}{8}$ $(3pi)/8$ . What is the area of the triangle?

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Answer 1 · 2017-03-30T11:37:50

The area of the triangle is $2.33 (2 d p)$ $2.33(2dp)$ sq.unit.

Explanation:

The angle between sides $A and C$ $A and C$ is $∠ b = \frac{13 π}{24} = \frac{13 \cdot 180}{24} = {97.5}^{0}$ $/_b=(13pi)/24 = (13*180)/24= 97.5^0$
The angle between sides $B and C$ $B and C$ is $∠ a = \frac{3 π}{8} = \frac{3 \cdot 180}{8} = {67.5}^{0}$ $/_a=(3pi)/8 = (3*180)/8= 67.5^0$

The angle between sides $A and B$ $A and B$ is $∠ c = 180 - (97.5 + 67.5) = 15^{0}$ $/_c=180-(97.5+67.5)= 15^0$

We know sides $A = 6, B = 3$ $A=6 , B=3$ and their included angle $∠ c = 15^{0}$ $/_c= 15^0$

The area of the triangle is $A_{t} = \frac{1}{2} \cdot A \cdot B \cdot sin c = \frac{1}{2} \cdot 6 \cdot 3 \cdot sin 15 = 9 \cdot sin 15 \approx 2.33 (2 d p)$ $A_t=1/2*A*B*sinc=1/2*6*3*sin15=9*sin15~~ 2.33(2dp)$ sq.unit [Ans]

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A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 3, respectively. The angle between A and C is $\frac{13 π}{24}$ $(13pi)/24$ and the angle between B and C is $\frac{3 π}{8}$ $(3pi)/8$ . What is the area of the triangle?

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Explanation:

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A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 3, respectively. The angle between A and C is 13π24(13pi)/24 and the angle between B and C is 3π8 (3pi)/8. What is the area of the triangle?

1 Answer

Explanation:

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A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 3, respectively. The angle between A and C is $\frac{13 π}{24}$ $(13pi)/24$ and the angle between B and C is $\frac{3 π}{8}$ $(3pi)/8$ . What is the area of the triangle?