David runs out of gas so he gets out of his car and walks 32 yards north and 85 blocks yards east. How far is he from his car if he walked back in a straight line? Round your answer to the nearest tenth
To find the distance between David's final location and his car, we can use the Pythagorean theorem. The theorem states that in a right-angled 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.
Let's calculate the distance using the theorem:
1. Convert the 32 yards and 85 blocks to the same unit. Assuming both are yards, we can proceed.
2. Define the two sides of the right-angled triangle:
- Side A: 32 yards (north)
- Side B: 85 yards (east)
3. Use the Pythagorean theorem:
Hypotenuse^2 = A^2 + B^2
Distance^2 = 32^2 + 85^2
Distance^2 = 1024 + 7225
Distance^2 = 8249
4. Calculate the square root of both sides to find the distance:
Distance = √8249
Distance ≈ 90.9 yards (rounding to the nearest tenth)
Therefore, David is approximately 90.9 yards away from his car when he walks back in a straight line.
To find the distance between David's current position and his car, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length 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, David creates a right triangle with the distance he walked north, the distance he walked east, and the direct distance back to his car. The distance he walked north and east is represented by the legs of the triangle, and the distance to his car is represented by the hypotenuse.
To calculate the distance to his car, we can use the following steps:
1. Calculate the square of the distance walked north:
(Distance north)² = 32² = 1024 yards²
2. Calculate the square of the distance walked east:
(Distance east)² = 85² = 7225 yards²
3. Add the squares of the two distances:
(Distance north)² + (Distance east)² = 1024 + 7225 = 8249 yards²
4. Take the square root of the sum to find the distance to his car:
Distance to car = √8249 ≈ 90.9 yards
Therefore, David is approximately 90.9 yards away from his car when he walks back in a straight line.