Sam S.

asked • 05/30/17

Which set of lengths will form a triangle with the greater area?

Using trigonometric methods (law of cosine/sine) or cosine/sine/tangent, determine which set of lengths will form a triangle with the greater area? Show work for both sets.
 
Set #1) 8 feet, 7 feet, and 12 feet. 
 
Set #2) 8 feet, 6 feet, and 12 feet. 

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Kenneth S. answered • 05/30/17

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The mere act of attempting to draw these triangles reveals that the first one has the larger area. Begin with the base, 12 ft in length. Now connect the other two sides to opposite ends of this base and wiggle them so that they intersect at a point above the base. It must be obvious that the first set of sides is the greater.
 
As for computing areas, the best (easiest) way of computing areas would be to use Heron's formula.
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Sam S.

Thanks! But our teacher has advised us to use what we've learned about so far and we've been taught the law of sines, cosines, and basic cosine/tangent/sine. 
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05/30/17

Kenneth S.

Please inform your teacher (if necessary) that Common Sense must never be ruled out. Therefore my reasoning in my first paragraph settles the question definitively.  The question DOES NOT ask for any areas.  You (and I) can tell which triangle will have the greater area.
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05/30/17

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