A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 7, respectively. The angle between A and C is $\frac{π}{4}$ $(pi)/4$ and the angle between B and C is $\frac{2 π}{3}$ $(2pi)/3$ . 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 12 and 7, respectively. The angle between A and C is $\frac{π}{4}$ $(pi)/4$ and the angle between B and C is $\frac{2 π}{3}$ $(2pi)/3$ . What is the area of the triangle?

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Answer 1 · 2016-10-31T11:30:21

Area of the triangle is $10.87 (2 d p) u n i t^{2}$ $10.87(2dp) unit^2$

Explanation:

The angle between sides A and C is $∠ b = \frac{π}{4} = \frac{180}{4} = 45^{0}$ $/_b=pi/4=180/4=45^0$
The angle between sides B and C is $∠ a = \frac{2 π}{3} = \frac{2 \cdot 180}{3} = 120^{0}$ $/_a=(2pi)/3=(2*180)/3=120^0$
The angle between sides A and B is $∠ c = 180 - ((45 + 120) = 15^{0}$ $/_c=180-((45+120)=15^0$
Now we know sides $A = 12; B = 7$ $A=12 ; B=7$ and their included angle $∠ c = 15^{0}$ $/_c=15^0$
So area of the triangle is $A_{t} = \frac{1}{2} \cdot A \cdot B \cdot sin c = \frac{1}{2} \cdot 12 \cdot 7 \cdot sin 15 = 10.87 (2 d p) u n i t^{2}$ $A_t=1/2*A*B*sinc= 1/2*12*7*sin15=10.87(2dp) unit^2$ [Ans]

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A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 7, respectively. The angle between A and C is $\frac{π}{4}$ $(pi)/4$ and the angle between B and C is $\frac{2 π}{3}$ $(2pi)/3$ . 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 12 and 7, respectively. The angle between A and C is π4(pi)/4 and the angle between B and C is 2π3 (2pi)/3. 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 12 and 7, respectively. The angle between A and C is $\frac{π}{4}$ $(pi)/4$ and the angle between B and C is $\frac{2 π}{3}$ $(2pi)/3$ . What is the area of the triangle?