Question

Jose draws AABC. AB has a length of 10 inches and BC has a length of 15 inches. Determine whether each measurement could be the length of AC. Choose Yes or No for each measurement. A Yes B No 5. 4 inches 6. 15 inches Yes No 7. 23 inches Yes No 8. 5 inches Yes No​

Answer 1

Answer: The length of AC should be between 5 inches and 25 inches

Step-by-step explanation:

Jose in this problem draws a triangle, AABC.

We know the length of two sides of the triangle:

AB = 10 inches

BC = 15 inches

The length of the third side in a generic triangle can be calculated using the cosine theorem: where

a, b, c are the three sides

is the angle opposite to side

Looking at the formula, we observe that:

- The maximum value for  is obtained for , so that . In this case, the length of the missing side  (AC, in this case) is

So, the length of AC must be between 5 and 25 inches.