A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 7, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{11 π}{24}$ $(11pi)/24$ . 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 3 and 7, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{11 π}{24}$ $(11pi)/24$ . What is the area of the triangle?

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Answer 1 · 2016-02-21T20:48:42

≈ 7.42 square units

Explanation:

The area can be calculated using $\frac{1}{2} A B sin θ$ $1/2 ABsintheta$
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 $= π$ $= pi$

hence the angle between A and B $= π - (\frac{7 π}{24} + \frac{11 π}{24})$ $= pi - ((7pi)/24 +(11pi)/24)$

$= π - \frac{18 π}{24} = \frac{6 π}{24} = \frac{π}{4}$ $= pi - (18pi)/24 = (6pi)/24 = pi/4$

$\Rightarrow area = \frac{1}{2} \times 3 \times 7 \times sin (\frac{π}{4}) \approx 7.42 square units$ $rArr " area" = 1/2xx3xx7xxsin(pi/4) ≈ 7.42" square units"$

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A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 7, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{11 π}{24}$ $(11pi)/24$ . 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 3 and 7, respectively. The angle between A and C is 7π24(7pi)/24 and the angle between B and C is 11π24 (11pi)/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 3 and 7, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{11 π}{24}$ $(11pi)/24$ . What is the area of the triangle?