Question

1. suppose greenville, rock hill, and columbia form a right triangle. what is the distance from columbia to greenville?

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 80\) (distance from Greenville to Rock Hill), \(b=68\) (distance from Rock Hill to Columbia). According to the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), where \(c\) is the distance from Columbia to Greenville.

$$c^{2}=80^{2}+68^{2}$$

Step2: Calculate \(a^{2}\) and \(b^{2}\)

$$80^{2}=6400$$

,

$$68^{2}=4624$$

$$c^{2}=6400 + 4624$$

Step3: Sum the values

$$c^{2}=11024$$

Step4: Find \(c\)

$$c=\sqrt{11024}\approx105$$

Answer:

The distance from Columbia to Greenville is approximately \(105\) miles.