A long-distance runner runs 5 miles south and then 8 miles east. How far is the runner from the starting
point? Round your answer to thousandths
Use the Pythagorean theorem. The distance ftom runner to starting point is the hypotenuse. The other two sides of the triangle are perpendicular.
A cylindrical jelly jar is 5 inches across the top and about 10 inches high. How many cubic inches of jelly
could it hold (to the nearest hundredth)?
To find the distance from the starting point, we can use the Pythagorean theorem, which 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 lengths of the other two sides.
In this case, the 5-mile south run forms one side of the right triangle, and the 8-mile east run forms the other side. The distance from the starting point to the current position of the runner represents the hypotenuse.
To calculate the distance, we can use the formula: distance = sqrt((side1)^2 + (side2)^2).
In this case, side1 = 5 miles and side2 = 8 miles.
Using the formula, we can calculate the distance:
distance = sqrt((5)^2 + (8)^2)
= sqrt(25 + 64)
= sqrt(89)
≈ 9.434 (rounded to thousandths)
Therefore, the runner is approximately 9.434 miles away from the starting point.