Question

to get from home to his friend elises house, wyatt would have to walk 2.7 miles due north. to get from home to his friend justins house, wyatt would have to walk 2.3 miles due east. what is the straight - line distance between elises house and justins house? if necessary, round to the nearest tenth. miles

Explanation:

Step1: Identify the right - angled triangle

The path from home to Elise's house, from home to Justin's house, and the straight - line between Elise's and Justin's house form a right - angled triangle. The two legs of the right - angled triangle have lengths $a = 2.7$ miles and $b=2.3$ miles.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem for a right - angled triangle is $c=\sqrt{a^{2}+b^{2}}$, where $c$ is the hypotenuse (the straight - line distance between Elise's and Justin's house), $a = 2.7$ and $b = 2.3$. So $c=\sqrt{(2.7)^{2}+(2.3)^{2}}$.

Step3: Calculate the squares

$(2.7)^{2}=2.7\times2.7 = 7.29$ and $(2.3)^{2}=2.3\times2.3 = 5.29$. Then $a^{2}+b^{2}=7.29 + 5.29=12.58$.

Step4: Calculate the square root

$c=\sqrt{12.58}\approx3.5$

Answer:

$3.5$