Question

from her house, ava could drive due north to get to her parents house or she could drive due east to get to her grandparents house. it is 3 miles from avas house to her parents house and a straight - line distance of 4 miles from her parents house to her grandparents house. how far is ava from her grandparents house? if necessary, round to the nearest tenth.

Explanation:

Step1: Identify right - triangle

The paths form a right - triangle. Let the distance from Ava's house to her parents' house be $a = 3$ miles, and the straight - line distance from her parents' house to her grandparents' house be $c = 4$ miles. We want to find the distance $b$ from Ava's house to her grandparents' house.

Step2: Apply Pythagorean theorem

According to the Pythagorean theorem $c^{2}=a^{2}+b^{2}$. We can rewrite it to solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute values

Substitute $a = 3$ and $c = 4$ into the formula: $b=\sqrt{4^{2}-3^{2}}=\sqrt{16 - 9}=\sqrt{7}\approx2.6$ miles.

Answer:

$2.6$