Question

salemburg is 17 miles south of linbrooke, and linbrooke is 5 miles west of pueblo. Carson lives nine miles north of linbrooke. how many miles is it from carson house to Salemburg through pueblo “as the crow flies”

Answer 1

Check the picture below.

so then, let's use the pythagorean theorem to find "x" and "y", and the distance is just x+y.

`\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=√(a^2+b^2) \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{9}\\ b=\stackrel{opposite}{5}\\ \end{cases} \\\\\\ x=√(9^2+5^2)\implies x=√(81+25)\implies x=√(106) \\\\[-0.35em] ~\dotfill`

`\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=√(a^2+b^2) \qquad \begin{cases} c=\stackrel{hypotenuse}{y}\\ a=\stackrel{adjacent}{17}\\ b=\stackrel{opposite}{5}\\ \end{cases} \\\\\\ y=√(17^2+5^2)\implies y=√(289+25)\implies y=√(314) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{total distance}}{x+y}\implies √(106)+√(314)\qquad \approx 10.296+17.72\qquad \approx 28.016`