Question

brians house is due west of oxford and due south of hillsboro. oxford is 10 kilometers from brians house and 26 kilometers from hillsboro. how far is hillsboro from brians house, measured in a straight line? kilometers

Explanation:

Step1: Identify right - triangle

The positions of Brian's house, Oxford, and Hillsboro form a right - triangle. Let the distance between Brian's house and Oxford be $a = 10$ km, the distance between Oxford and Hillsboro be $c = 26$ km, and the distance between Brian's house and Hillsboro be $b$.

Step2: Apply Pythagorean theorem

According to the Pythagorean theorem $c^{2}=a^{2}+b^{2}$, so $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute values

Substitute $a = 10$ and $c = 26$ into the formula: $b=\sqrt{26^{2}-10^{2}}=\sqrt{(26 + 10)(26 - 10)}=\sqrt{36\times16}=\sqrt{576}=24$.

Answer:

24