Question

ASAP PLS! Three points determine △ABC. The distance between A and B is 22.2 feet. The distance between B and C is 9.9 feet.

What is the range for the distance between A and C?

The range of the distance from A to C is greater than ------
feet and less than -------
feet.

Answer 1

The range of the distance from A to C is greater than 12.3 feet and less than 32.1 feet.

Explanation:

Triangle Inequality Theorem

The measure of any side of a triangle must be less than the sum of the measures of the other two sides.

Given:

• AB = 22.2 ft
• BC = 9.9 ft

Taking AB to be the longest side of the triangle.

The measure of AB must be less than the sum of AC and BC:

⇒ AB < AC + BC

⇒ 22.2 < AC + 9.9

⇒ 22.2 - 9.9 < AC

⇒ 12.3 < AC

⇒ AC > 12.3 ft

Taking AC to be the longest side of the triangle.

The measure of AC must be less than the sum of AB and BC:

⇒ AC < AB + BC

⇒ AC < 22.2 + 9.9

⇒ AC < 32.1 ft

Therefore, the range of the distance from A to C is greater than 12.3 feet and less than 32.1 feet.