Given that two sides of a triangle are 20 and 66. Find the range of possible measures for the third side, s.

a. 20<s<66
b. 46<s<86
c. 20<s<86
d.46<s<66

If you could tell me how to do this problem, i could do my next four.

In the extreme cases, the length of the third side can be either the sum or the difference of the two other side lengths. That is when the triangle reduces to a straight line.

Let that fact guide you in your answer.

tch a 45 degree -45 degree -90 degree triangle. how are the two legs related to each other? How is the hypotenuse related to a leg?

To find the possible range of measures for the third side, s, of a triangle with given side lengths of 20 and 66, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So, in this case, we can write the following inequality:

20 + 66 > s

Simplifying the inequality, we get:

86 > s

Therefore, the upper limit for the range of possible measures for s is 86.

Similarly, applying the triangle inequality theorem, we can write the second inequality:

66 - 20 < s

Simplifying the inequality, we get:

46 < s

Therefore, the lower limit for the range of possible measures for s is 46.

Combining both inequalities, we have:

46 < s < 86

Hence, the correct answer is option b) 46 < s < 86.