Oliver M.

asked • 04/26/17

Advanced trig problem I'm having an issue with.

Ok so on a math work sheet we had a problem where there was two side lengths of a triangle, 63 and 91. The third side was only described as being traveled across by a plane with an average of 300mph??? How do I find the length of the third side, also its worth mentioning that no angle measures were giv

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Inactive Tutor answered • 04/26/17

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Hi Oliver,
I don't think this question can be solved. Since there are no angles given, you can have many different triangles using those two length measures and combinations of different angles and the unknown side length. For example, the angle between the sides whose lengths are given can be obtuse or acute, which would significantly change the length measure of the other side.
 
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Inactive Tutor

Hi again Oliver,
 
I need to correct myself. A range can be given for the length of the third side using the triangle inequality theorem. This theorem states that "any side of a triangle must be shorter than the other two sides added together". Please note that this is true regardless of any angle measure or lack of it. 
If we let the length of the third side x, then
x < 91+63  --> x < 154
63 < 91+x  --> -28 < x
91 < 63+x  -->  28 < x
From the above inequalities, we get 28 < x < 154. Any value within this range can be the length of the third side. 
 
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04/26/17

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