A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 14, respectively. The angle between A and C is $\frac{17 π}{24}$ $(17pi)/24$ and the angle between B and C is $(π) 24$ $(pi)24$ . 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 14, respectively. The angle between A and C is $\frac{17 π}{24}$ $(17pi)/24$ and the angle between B and C is $(π) 24$ $(pi)24$ . What is the area of the triangle?

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Answer 1 · 2016-11-04T21:07:57

$\frac{1}{2} \cdot 6 \cdot 14 \cdot sin (\frac{π}{4}) = 21 \sqrt[2]{2}$ $1/2*6*14*sin(pi/4)=21root(2)2$

Explanation:

The angle between A and B is given by $θ = π - 17 \frac{π}{24} - \frac{π}{24} = \frac{24 π - 18 π}{24} = \frac{π}{4}$ $theta=pi-17pi/24-pi/24=(24pi-18pi)/24=pi/4$

The area is given by $\frac{1}{2} \cdot A \cdot B \cdot sin (θ)$ $1/2*A*B*sin(theta)$

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A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 14, respectively. The angle between A and C is $\frac{17 π}{24}$ $(17pi)/24$ and the angle between B and C is $(π) 24$ $(pi)24$ . 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 14, respectively. The angle between A and C is (17pi)/2417π24(17pi)/24 and the angle between B and C is (pi)24(π)24 (pi)24. 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 14, respectively. The angle between A and C is $\frac{17 π}{24}$ $(17pi)/24$ and the angle between B and C is $(π) 24$ $(pi)24$ . What is the area of the triangle?