Question

kevin rode his bike 2 miles east and 6 miles north from his home to the movie theater, forming a right angle. how far is the movie theater from kevins home? 5.66 miles 8 miles 12 miles 6.32 miles

Explanation:

Step1: Identify the right - triangle sides

The two legs of the right - triangle are $a = 2$ miles and $b = 6$ miles.

Step2: Apply the Pythagorean theorem

The distance $d$ (hypotenuse) from Kevin's home to the movie theater is given by $d=\sqrt{a^{2}+b^{2}}=\sqrt{2^{2}+6^{2}}=\sqrt{4 + 36}=\sqrt{40}$.

Step3: Simplify the square - root

$\sqrt{40}=\sqrt{4\times10}=2\sqrt{10}\approx2\times3.162 = 6.32$ miles.

Answer:

6.32 miles