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

In a right - triangle, if \(a = 80\) (distance from Greenville to Rock Hill) and \(b=68\) (distance from Rock Hill to Columbia), and \(c\) is the distance from Columbia to Greenville. By the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\).

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

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

$$80^{2}=6400$$

,

$$68^{2}=4624$$

Step3: Sum \(a^{2}\) and \(b^{2}\)

$$6400 + 4624=11024$$

Step4: Take the square root

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

(rounded to the nearest whole number)

Answer:

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