Virginia Mathematics Teacher Spring 2017

So l ut i ons t o Fa l l 2016 HEXA Cha l l enge Probl ems

SOLUTION: Let’s label the measures of the angles of the triangle as α, β, and γ. We know that The value of any angle may vary between 0 and 180 degrees (In the extreme cases, creating degenerate tri- angles). If one of the angles in a triangle is greater than 90 degrees, then the triangle is obtuse. For obtuse triangles, . The shaded area in the figure below represents the set of all obtuse triangles. The axes are α and β. As you can tell, each of the shaded regions are congruent with each other and represent 1/4 th of the total area. Therefore, the chance of any triangle being obtuse is , or 75%.

January Solve the following equation:

SOLUTION: To solve algebraically:

Virginia Mathematics Teacher vol. 43, no. 2

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