If you drive 16
miles south, then make a left turn and drive 12
miles east, how far are you, in a straight line, from your starting point? Use the Pythagorean Theorem to solve the problem. Use a calculator to find square roots, rounding to the nearest tenth as needed.
We can use the Pythagorean theorem to solve this problem. Let's call the distance we are looking for "d".
To use the Pythagorean theorem, we need to know the lengths of two sides of a right triangle. We can create a right triangle by drawing a line from our starting point to our ending point (which is 16 miles south and 12 miles east of our starting point).
We can use the 16 miles and 12 miles as the lengths of the legs of our right triangle. The distance we are looking for (d) is the length of the hypotenuse of the right triangle.
Using the Pythagorean theorem, we can write:
d^2 = 16^2 + 12^2
d^2 = 256 + 144
d^2 = 400
Taking the square root of both sides, we get:
d = √400
d = 20
So we are 20 miles from our starting point in a straight line.
To use the Pythagorean Theorem, we need to find the lengths of the two legs of a right triangle formed by driving 16 miles south and then 12 miles east.
The distance driven south is one leg of the triangle, so let's call it leg A. The distance driven east is the other leg of the triangle, so let's call it leg B.
Leg A = 16 miles
Leg B = 12 miles
Using the Pythagorean Theorem, we can find the length of the hypotenuse, which is the straight-line distance from the starting point.
The Pythagorean Theorem states that the square of the length of the hypotenuse (C) is equal to the sum of the squares of the lengths of the two legs (A and B).
C^2 = A^2 + B^2
Substituting the values we have:
C^2 = 16^2 + 12^2
C^2 = 256 + 144
C^2 = 400
To find C, we take the square root of both sides of the equation:
C = √400 = 20
Therefore, the straight-line distance from the starting point is 20 miles.