Question

use the pythagorean theorem.
leine and laura began hiking from their campground. laura headed south while leine headed east. laura walked 16 mi and leine walked 30 mi. how far apart were they when they stopped walking?
laura and leine were
mi apart when they stopped walking.

Explanation:

Step1: Recall the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 16\) (distance Laura walked) and \(b = 30\) (distance Leine walked).

Step2: Substitute the values into the formula

Substitute \(a = 16\) and \(b = 30\) into \(c^{2}=a^{2}+b^{2}\). So, \(c^{2}=16^{2}+30^{2}\).
Calculate \(16^{2}=256\) and \(30^{2}=900\). Then \(c^{2}=256 + 900=1156\).

Step3: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (distance), \(c=\sqrt{1156}\). And \(\sqrt{1156}=34\).

Answer:

34