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

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

Step-by-step 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:

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

- The minimum value for is obtained for , for which , so in this case the length of AC is

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

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

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