Question

How do you find the diagonal distance when a girl hikes 3 miles north and 4 miles east?

Answer 1

Think of this as a triangle. The height is 3 miles and the side is 4. It's a 3,4,5 triangle. You are using the Pyhtagorean Theorem to find the hypotenuse, or the diagonal distance. 3 squared plus 4 squared equals the perfect square of the distance. So, 9 plus 16 equals 25. Square root that, and you get 5. So, the diagonal distance is 5 miles.

Answer 2

We can find the diagonal distance using the Pythagorean Theorem (PT). PT is a formula that calculates the diagonal distance (c) when it knows the value of north/south (a) and east/west (b).

PT is a²+b²=c², so we simply need to substitute 3 and 4 in for a and b, respectively.

a²+b²=c²
3²+4²=c²
9+16=c²
25=c²
$\sqrt{25}= \sqrt{c^{2}}$
5=c

Using the math above, we can see the diagonal distance from her starting point is 5 miles.