an orienteer runs 300m north and then 400m to the southeast (at a 45 degree angle to north). if he runs at a constant speed, how far away is he from the starting position?
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To find how far away the orienteer is from the starting position, we can use the Pythagorean theorem.
First, let's break down the orienteer's movement into their north and east components:
North: 300m
East: 400m (at a 45-degree angle to the north)
We can calculate the distance traveled by the orienteer using these components.
Using the Pythagorean theorem:
distance^2 = north^2 + east^2
distance^2 = 300^2 + 400^2
distance^2 = 90000 + 160000
distance^2 = 250000
Taking the square root of both sides:
distance = √250000
Simplifying:
distance ≈ 500 meters
Therefore, the orienteer is approximately 500 meters away from the starting position.
To find out how far away the orienteer is from the starting position, you 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 lengths of the other two sides.
In this case, we have a right triangle with sides of 300m and 400m. The diagonal, or hypotenuse, represents the distance the orienteer is away from the starting position. Let's call this distance 'd'.
To find 'd', we can use the Pythagorean theorem:
d^2 = 300^2 + 400^2
Calculating this equation:
d^2 = 90000 + 160000
d^2 = 250000
Now, take the square root of both sides to solve for 'd':
d = √250000
d ≈ 500
Therefore, the orienteer is approximately 500 meters away from the starting position.