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Silvergrove is $15$ kilometers due north of the airport, and Weston is $8$ kilometers due east of the airport. How far apart are Silvergrove and Weston? $\newline$ $\newline$ $\_\_\_\_$ kilometers

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Pythagorean theorem: word problems

Full solution

Q. Silvergrove is

15

kilometers due north of the airport, and Weston is

8

kilometers due east of the airport. How far apart are Silvergrove and Weston?

\newline

\newline

\_\_\_\_

kilometers

Identify Problem Setup: Step $1$ : Identify the problem setup and the triangle formed. $\newline$ Silvergrove is directly north of the airport, and Weston is directly east of the airport. This forms a right triangle with Silvergrove and Weston at the ends of the hypotenuse.
Assign Values to Legs: Step $2$ : Assign values to the legs of the triangle. $\newline$ The distance from the airport to Silvergrove (north-south leg) is $15\,\text{km}$ , and the distance from the airport to Weston (east-west leg) is $8\,\text{km}$ .
Apply Pythagorean Theorem: Step $3$ : Apply the Pythagorean Theorem to find the distance between Silvergrove and Weston. $\newline$ Using the formula $a^2 + b^2 = c^2$ , where $a = 15$ km and $b = 8$ km, calculate $c$ , the distance between Silvergrove and Weston. $\newline$ $15^2 + 8^2 = c^2$ $\newline$ $225 + 64 = c^2$ $\newline$ $289 = c^2$
Solve for Hypotenuse: Step $4$ : Solve for $c$ , the hypotenuse. $\newline$ Take the square root of $289$ to find $c$ . $\newline$ $\sqrt{289} = 17$

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