Question

michael goes for a bike ride. he rides 12 miles due east. he then rides due north for some distance and stops. when he stops riding his bike, michael is exactly 20 miles away from where he began. a diagram of michaels bike ride is shown. what is the distance, in miles, that michael rides due north? miles

Explanation:

Step1: Apply Pythagorean theorem

Let the distance ridden north be $x$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 20$ (hypotenuse) and $a = 12$ (one - side), so $12^{2}+x^{2}=20^{2}$.

Step2: Simplify the equation

$144 + x^{2}=400$. Then $x^{2}=400 - 144$.

Step3: Calculate $x^{2}$

$x^{2}=256$.

Step4: Solve for $x$

$x=\sqrt{256}=16$.

Answer:

16