Question

darren is playing hide - and - seek with jason and hannah. jason is hiding 8 meters south of darren, and hannah is hiding 3 meters east of jason. how far apart are darren and hannah? if necessary, round to the nearest tenth.

Explanation:

Step1: Identify as right - triangle problem

We can consider the positions as a right - triangle. The vertical side (opposite side) of the right - triangle is 8 meters (distance between Darren and Jason) and the horizontal side (adjacent side) is 3 meters (distance between Jason and Hannah).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $a = 8$ and $b = 3$. So $c=\sqrt{a^{2}+b^{2}}=\sqrt{8^{2}+3^{2}}$.

Step3: Calculate the value

$c=\sqrt{64 + 9}=\sqrt{73}\approx8.5$

Answer:

8.5