David runs out of gas so he gets out of his car and walks 32 miles north and 85 blocks yards East how far is he from his car if you walk back in a straight line round your answer to the nearest 10th
To find the distance David is from his car after walking back, we need to use the Pythagorean theorem.
Given that David walks 32 miles north and 85 yards east, we can treat this as a right triangle with the distance he walks north as the vertical leg (32 miles) and the distance he walks east as the horizontal leg (85 yards).
Using the theorem:
Distance^2 = Vertical leg^2 + Horizontal leg^2
Distance^2 = (32 miles)^2 + (85 yards)^2
Distance^2 = 1024 miles^2 + 7225 yards^2
To compare the units, we need to convert yards to miles:
1 mile = 1760 yards, so 85 yards = 85/1760 miles = 0.0483 miles (rounded to 4 decimal places)
Distance^2 = 1024 miles^2 + (0.0483 miles)^2
Distance^2 = 1024 miles^2 + 0.0023329 miles^2
Distance^2 = 1024.0023329 miles^2
Taking the square root of both sides to find the distance:
Distance = √(1024.0023329 miles^2)
Distance ≈ 32.0 miles (rounded to the nearest tenth)
Therefore, David is approximately 32.0 miles from his car when he walks back in a straight line.