Question

1. scott wants to swim across a river that is 400 meters wide. he begins swimming perpendicular to the shore he started from but ends up 100 meters down river from where he started because of the current. how far did he actually swim from his starting point?

Explanation:

Step1: Identify the right - angled triangle

The width of the river forms one leg ($a = 400$ meters) and the distance downstream forms the other leg ($b = 100$ meters) of a right - angled triangle. The actual distance Scott swam is the hypotenuse $c$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 400$ and $b = 100$ into the formula: $c=\sqrt{400^{2}+100^{2}}=\sqrt{160000 + 10000}=\sqrt{170000}$.

Step3: Simplify the square - root

$\sqrt{170000}=100\sqrt{17}\approx412.31$ meters.

Answer:

$100\sqrt{17}\approx412.31$ meters