A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 12, respectively. The angle between A and C is $\frac{11 π}{24}$ $(11pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . 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 5 and 12, respectively. The angle between A and C is $\frac{11 π}{24}$ $(11pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . What is the area of the triangle?

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Answer 1 · 2016-02-21T20:17:56

≈ 29 square units

Explanation:

The area of the triangle can be found by using $\frac{1}{2} A B sin θ$ $1/2ABsintheta$
where $θ is the angle between A and B$ $theta" is the angle between A and B "$

The sum of the 3 angles in a triangle is $π$ $pi$

The angle between A and B = $π - (\frac{11 π}{24} + \frac{π}{8})$ $pi - ((11pi)/24 + pi/8 )$

$= π - \frac{14 π}{24} = \frac{5 π}{12}$ $= pi - (14pi)/24 = (5pi)/12$

area = $\frac{1}{2} \times 5 \times 12 \times sin (\frac{5 π}{12}) \approx 29 square units$ $1/2xx5xx12xxsin((5pi)/12) ≈ 29" square units"$

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A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 12, respectively. The angle between A and C is $\frac{11 π}{24}$ $(11pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . 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 5 and 12, respectively. The angle between A and C is 11π24(11pi)/24 and the angle between B and C is π8 (pi)/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 5 and 12, respectively. The angle between A and C is $\frac{11 π}{24}$ $(11pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . What is the area of the triangle?