Answer :
To find how far the helicopter is from its starting point after it rose vertically and then flew east, we can use the Pythagorean theorem. Here's a step-by-step explanation:
1. Identify the Problem:
- The helicopter rises vertically 325 meters.
- Then it flies east 500 meters.
- We need to find the distance from the starting point to the final position of the helicopter.
2. Apply the Pythagorean Theorem:
- The vertical rise and the horizontal flight form a right triangle with the distance from the starting point as the hypotenuse.
- According to the Pythagorean theorem:
[tex]\[
(\text{vertical distance})^2 + (\text{horizontal distance})^2 = (\text{hypotenuse})^2
\][/tex]
3. Insert the Given Values:
- Vertical distance: 325 meters
- Horizontal distance: 500 meters
4. Calculate the Hypotenuse:
- Calculate the square of the vertical distance: [tex]\(325^2 = 105625\)[/tex]
- Calculate the square of the horizontal distance: [tex]\(500^2 = 250000\)[/tex]
- Add these squares together: [tex]\(105625 + 250000 = 355625\)[/tex]
5. Find the Square Root:
- Take the square root of 355625 to find the hypotenuse, which represents the distance from the starting point:
[tex]\[
\sqrt{355625} \approx 596.34
\][/tex]
So, the helicopter is approximately 596.34 meters away from its starting point.
1. Identify the Problem:
- The helicopter rises vertically 325 meters.
- Then it flies east 500 meters.
- We need to find the distance from the starting point to the final position of the helicopter.
2. Apply the Pythagorean Theorem:
- The vertical rise and the horizontal flight form a right triangle with the distance from the starting point as the hypotenuse.
- According to the Pythagorean theorem:
[tex]\[
(\text{vertical distance})^2 + (\text{horizontal distance})^2 = (\text{hypotenuse})^2
\][/tex]
3. Insert the Given Values:
- Vertical distance: 325 meters
- Horizontal distance: 500 meters
4. Calculate the Hypotenuse:
- Calculate the square of the vertical distance: [tex]\(325^2 = 105625\)[/tex]
- Calculate the square of the horizontal distance: [tex]\(500^2 = 250000\)[/tex]
- Add these squares together: [tex]\(105625 + 250000 = 355625\)[/tex]
5. Find the Square Root:
- Take the square root of 355625 to find the hypotenuse, which represents the distance from the starting point:
[tex]\[
\sqrt{355625} \approx 596.34
\][/tex]
So, the helicopter is approximately 596.34 meters away from its starting point.
