Question

1. daniel rides his bike 21 km west and then 18 km north. how far is he from his starting point? round to the nearest hundredth.

Explanation:

Step1: Identify as right - triangle problem

The west - east and north - south directions are perpendicular. The distances of 21 km west and 18 km north form the two legs of a right - triangle. We can use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 21$ km and $b = 18$ km, and $c$ is the distance from the starting point.

Step2: Substitute values into Pythagorean theorem

$c=\sqrt{21^{2}+18^{2}}$. First, calculate $21^{2}=21\times21 = 441$ and $18^{2}=18\times18 = 324$. Then $21^{2}+18^{2}=441 + 324=765$. So $c=\sqrt{765}$.

Step3: Calculate the square - root and round

$\sqrt{765}\approx27.66$ km.

Answer:

$27.66$ km