Question

You start driving north for 16 miles, turn right, and drive east for another 30 miles. How many miles must you travel to return directly back to your starting point?

Answer 1

Answer:

The distance traveled to return directly to the starting point = 34 miles.

Step-by-step explanation:

Given:

Distance covered in north = 16 miles

Distance covered in east = 30 miles

We have to find the displacement (the shortest distance).

Or

Distance traveled to return directly back to the starting point.

Let the origin be O $(0,0)$ and the distance covered in north be ON and distance covered from right to the east is NE.

Move rightward from N point to the right that is towards east direction.

N is a northern point and E is the eastern point.

ON = $16$ miles

NE = $30$ miles

We can imagine that it forms a right angled  triangle making 90 (deg) at N by joining E with O $(0,0)$,where OE is the

hypotenuse.

Applying Pythagoras formula.

Where,

Hypotenuse = $\sqrt{ON^2+NE^2}$

The distance traveled in returning back to the starting point is equivalent to the measure of the hypotenuse.

So,

Hypotenuse        = $\sqrt{16^2+30^2}$

                            = $\sqrt{256+900}$

                            = $\sqrt{1156}$

                            = $34$ miles

So the distance traveled to return directly to the starting point = 34 miles.