Math Geometry Question - Calculate triangle side...10 PTS!!!?

Let the third side in question be c. Then by using triangle inequality 3 times we get.

4+9>c that is 13>c or c<13

4+c>9 or 4+c-4>9-4 that is c>5

9+c>4- This one is a given since the lenght of side must be positive.

So the range for c is (5,13) with end points NOT included

that is 5<c<13

Impossible to give you exact values bud. The third side could be anywhere from just under 13 units (12.9999999999999) to just over 5 units (5.00000000000001).

Think about it like this:

If the 9 and 4 unit lines had an angle of 180 degrees between them then the distance from the two end points would be 13 units.

If the 9 and 4 unit lines had an angle of 0 degrees between them then the distance from the two end points would be 5 units.

So anything just smaller then 13 and just larger then 5 will make a triangle, because 13 units and 5 units will just give you lines.

Sorry if this is not clear. If you draw it out it will make a lot more sense.

5 < 3rd side < 13

Let the third side be s. The range of the possible length of the third side is:

(9 - 4) < s < (9 + 4)

5 < s < 13

It took me about a minute to solve this problem once I pictured the problem in my mind.

What do you know about a triangle? One thing is that all of the angles add up to 180 degrees.

So what is the minimum and maximum angle between the 9 unit and 4 unit sides?

If you think of the maximum, the largest the angle can be is a slight fraction below 180 degrees.

If you think of the minimum the smallest angle is a slight fraction above 0 degrees. Drawing it out you should find the answer easily.

The range must be greater than 5 units.

well the third side has to be 5 - 13 units long, i don't see what was so hard :|

It is 9.8488578. You find the hypotenuse, and that's it. (It would probably round to 10 or 9.8 if on homework)