A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 5, respectively. The angle between A and C is $\frac{5 π}{24}$ $(5pi)/24$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . 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 7 and 5, respectively. The angle between A and C is $\frac{5 π}{24}$ $(5pi)/24$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . What is the area of the triangle?

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Answer 1 · 2018-03-15T15:51:32

This triangle does not exist...

Explanation:

Just by looking at the angles, side A should correspond to the angle between side B and C, while side B should correspond to the angle between side A and C. Since side A is larger than side B but has a smaller angle corresponding to it, this triangle does not exist...

Proof with the Law of Sines:
$A = arcsin (\frac{sin B \cdot a}{b})$ $A= arcsin((SinB*a)/b)$
$A = arcsin ⎛ ⎜ ⎝ \frac{sin (\frac{5 π}{24}) \cdot 7}{5} ⎞ ⎟ ⎠ = 1.02 r a d$ $A= arcsin((Sin((5pi)/24)*7)/5)= 1.02 rad$
$\frac{π}{24} r a d \neq 1.02 r a d$ $pi/24 rad ≠ 1.02 rad$

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A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 5, respectively. The angle between A and C is $\frac{5 π}{24}$ $(5pi)/24$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . 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 7 and 5, respectively. The angle between A and C is 5π24(5pi)/24 and the angle between B and C is π24 (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 7 and 5, respectively. The angle between A and C is $\frac{5 π}{24}$ $(5pi)/24$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . What is the area of the triangle?