Let's consider a triangle ΔABC, with angle A = 71°, angle B = 37°, angle C = 72°. So, is this data sufficient to find the area of the ΔABC ? Is there any formula to do so or even a method ?

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    $\begingroup$ Consider an equilateral triangle with side length $1$. Compare the area of this triangle to an equilateral triangle with side lengths $100000$. Both triangles have the same trio of angles, but the one clearly has larger area. Two triangles who have the same angles will be "similar" but similarity doesn't imply the same area. $\endgroup$
    – JMoravitz
    Nov 4 '19 at 13:19
  • $\begingroup$ No, consider the dilation by a factor of $3$ on $ABC$. The new triangle has the same angles but different side lengths. Which implies different height and base which means different area. $\endgroup$ Nov 4 '19 at 13:20
  • $\begingroup$ In general (like in the title) it depends on geometry. E.g. on a sphere with a given radius it's enough to know the three angles. However the exact values you provided in the question body cannot form a triangle on a sphere. You most likely meant Euclidean geometry. If so, then the accepted answer is right. $\endgroup$ Nov 4 '19 at 13:59

When you scale the triangle the angles stay the same, while the area is changing.


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