You start driving east for 14 miles, turn left, and drive north for another 6 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.
We can use the Pythagorean theorem to find the straight line distance from the starting point:
c² = a² + b²
where c is the hypotenuse (the straight line distance), and a and b are the lengths of the other two sides of the right triangle formed by our driving directions. In this case:
a = 14 miles (east)
b = 6 miles (north)
c² = 14² + 6²
c² = 196 + 36
c² = 232
c ≈ 15.2
Therefore, our straight line distance from the starting point is approximately 15.2 miles. Rounded to the nearest tenth of a mile, the answer is 15.2.
To find the straight-line distance from the starting point to the end point, we can use the Pythagorean theorem.
Step 1: Start by drawing a diagram to visualize the scenario.
Starting point (A)
| 14 miles (east)
|
|
| (left turn)
|
|
End point (B)
| 6 miles (north)
Step 2: From the diagram, we can see that we have formed a right triangle with the starting point (A), end point (B), and a line connecting them as the hypotenuse.
Step 3: Using the Pythagorean theorem, we can calculate the length of the hypotenuse. The formula is given by:
c^2 = a^2 + b^2,
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides of the right triangle.
Step 4: In our case, the length of side a is 14 miles and the length of side b is 6 miles.
Plugging these values into the formula, we get:
c^2 = (14)^2 + (6)^2
c^2 = 196 + 36
c^2 = 232
Step 5: Taking the square root of both sides to find the length of the hypotenuse, we get:
c = √232 ≈ 15.2
Step 6: Round the length to the nearest tenth of a mile, which gives us:
The straight-line distance from the starting point to the end point is approximately 15.2 miles.
Thus, the straight-line distance from the starting point is approximately 15.2 miles.