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All the Angles

Pro Problems > Math > Algebra > Functions > Trigonometry > Solving Triangles > Side-Side-Side
 

All the Angles

Given that the sides of a triangle have lengths 4, 5, and 6, determine the sines of all three angles of the triangle.

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Problem by Mr. H

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The average of the lengths of the sides of a triangle is 20 units. The sides of the triangle are in arithmetic progression (the difference between the shortest side and the middle side is the same as the difference between the middle side and the longest side). The length of the shortest side is 13 units. What is the area of the triangle, as an exact value?

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