if AB = 24 and BC = 17 then what does AC equal?

Answer 1

If you have the measure of angle B (between AB and BC), then you can get an exact answer.

Otherwise, using the triangle inequality theorem (the sum of the lengths of any two sides of a triangle is greater than the length of the third side) you can find a range of values for the length of AC.

We know that either AB (24) or AC (our unknown) has to be the longest side in the triangle (because BC is already shorter than AB and therefore cannot be the longest).

If we assume AB is the longest, we can write the inequality:

AC + BC > AB

x + 17 > 24 and then solve for x/AC

-17 -17

x > 7

Now, on the other side, if we assume AC is the longest, we write:

AB + BC > AC

24 + 17 > x and then solve for x/AC

41 > x

So without knowing the measure of angle B, we can say that AC's length can be represented by

7 < AC < 41

Hope this helps! If you have any other questions feel free to reach out.