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The sides of a triangle have lengths 9 13 and 'k' where 'k' is an integer. For how many values of 'k' is the triangle obtuse?
Wiki User
∙ 15y ago
A few comments firstly.
* If the triangle were to be a right-angled one then K could equal sqrt(81 + 169) = 15.8.
* If K is equal to, or greater than 9 + 13 then it wouldn't be a triangle. * So if K > 15.8 then the angle opposite the it would be obtuse.
So, any value from among 16, 17, 18, 19, 20 , 21 and 22 would give an obtuse triangle
Furthermore, there is the 'other' triangle
* If the triangle were to be a right-angled one then K could equal sqrt(169 - 81) = 9.3
* If K is equal to, or less than 13 - 9 then it wouldn't be a triangle.
* So, if K > 4 the angle opposite 13 would be obtuse.
So, any value from among 5, 6, 7, 8 and 9 would also give an obtuse triangle.
So the answer is 12 values.
Wiki User
∙ 15y ago
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