You and a friend go biking. You bike 12 miles north and 2 miles east. What is the straight-line distance from your starting point? Round answer to the nearest hundredths
You need the hypotenuse of a right angle triangle.
a^2 + b^2 = c^2
12^2 + 2^2 = c^2
144 + 4 = c^2
148 = c^2
12.165 = c
12.17 = c
To find the straight-line distance from your starting point to your ending point, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the distance biked north and east form two sides of a right triangle, and the straight-line distance is the hypotenuse.
Using this information, we can calculate the straight-line distance as follows:
1. Start by squaring the distance biked north: 12^2 = 144.
2. Next, square the distance biked east: 2^2 = 4.
3. Add the two squared distances together: 144 + 4 = 148.
4. Finally, take the square root of the sum to find the straight-line distance:
√148 ≈ 12.166.
Rounding this answer to the nearest hundredth, the straight-line distance from your starting point is approximately 12.17 miles.