A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 5, respectively. The angle between A and C is $\frac{3 π}{8}$ $(3pi)/8$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . 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 4 and 5, respectively. The angle between A and C is $\frac{3 π}{8}$ $(3pi)/8$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . What is the area of the triangle?

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Answer 1 · 2016-02-21T10:25:49

area ≈ 9.66 square units

Explanation:

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

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

Then the angle $θ = π - (\frac{3 π}{8} + \frac{5 π}{24})$ $theta = pi -((3pi)/8 + (5pi)/24)$

$\Rightarrow θ = π - \frac{7 π}{12} = \frac{5 π}{12}$ $rArr theta = pi - (7pi)/12 = (5pi)/12$

$\Rightarrow area = \frac{1}{2} \times 4 \times 5 \times sin (\frac{5 π}{12}) \approx 9.66$ $rArr "area " = 1/2 xx 4 xx 5 xx sin((5pi)/12) ≈ 9.66$

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A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 5, respectively. The angle between A and C is $\frac{3 π}{8}$ $(3pi)/8$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . 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 4 and 5, respectively. The angle between A and C is 3π8(3pi)/8 and the angle between B and C is 5π24 (5pi)/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 4 and 5, respectively. The angle between A and C is $\frac{3 π}{8}$ $(3pi)/8$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . What is the area of the triangle?