Question

1. nina wants to swim across a river that is 150 meters wide. she begins swimming perpendicular to the shore. due to the current, when she makes it across the river, she is 60 meters down - shore from her starting point. how many meters did she actually swim across the river?

Explanation:

Step1: Identify the right - angled triangle

The width of the river forms one side of a right - angled triangle ($a = 150$ meters), and the distance downstream forms the other side ($b = 60$ meters). The actual distance she swims across the river is the hypotenuse of the right - angled triangle.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$, where $a = 150$ and $b = 60$. So $c=\sqrt{150^{2}+60^{2}}=\sqrt{22500 + 3600}=\sqrt{26100}$.

Step3: Calculate the value of the hypotenuse

$\sqrt{26100}\approx161.55$ meters.

Answer:

Approximately 161.55 meters