Question

Jose draws abc. 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

Answer 1

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

Explanation:

Jose in this problem draws a triangle, ABC.

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:

`a=√(b^2+c^2-2bc cos \alpha)`

where

a, b, c are the three sides

`\alpha` is the angle opposite to side
`a`

Looking at the formula, we observe that:

- The maximum value for
`a` is obtained for
`\alpha=180^(\circ)`, so that
`cos \alpha = -1`. In this case, the length of the missing side (AC, in this case) is

`AC=√(10^2+15^2-2(10)(15)(-1))=25 in`

- The minimum value for
`a` is obtained for
`\alpha=0^(\circ)`, for which
`cos \alpha =1`, so in this case the length of AC is

`AC=√(10^2+15^2-2(10)(15)(1))=5 in`

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