Question

kensington is 5.8 miles due north of the airport, and fairview is 5.8 miles due east of the airport. how far apart are kensington and fairview? if necessary, round to the nearest tenth.
□ miles

Explanation:

Step1: Identify the triangle type

The positions of Kensington, Fairview, and the airport form a right triangle, where the two legs (distance from airport to Kensington and airport to Fairview) are both 5.8 miles. Let \( a = 5.8 \), \( b = 5.8 \), and we need to find the hypotenuse \( c \).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right triangle, \( c = \sqrt{a^2 + b^2} \). Substituting \( a = 5.8 \) and \( b = 5.8 \):
\[
c = \sqrt{(5.8)^2 + (5.8)^2} = \sqrt{2 \times (5.8)^2} = 5.8\sqrt{2}
\]

Step3: Calculate the value

First, calculate \( \sqrt{2} \approx 1.4142 \). Then, multiply by 5.8:
\[
5.8 \times 1.4142 \approx 8.2
\]

Answer:

8.2