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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No added it used Pythagoras
To find the distance the orienteer is from the starting position, you can use the Pythagorean theorem.
The orienteer runs 300m north, forming the vertical side of the right triangle.
The orienteer then runs 400m to the southeast at a 45-degree angle, forming the diagonal side of the right triangle.
Using the Pythagorean theorem, we can find the length of the hypotenuse, which represents the distance from the starting position.
The Pythagorean theorem states that in a right triangle:
c^2 = a^2 + b^2
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
In this case, the lengths of the two sides are 300m and 400m.
c^2 = 300^2 + 400^2
c^2 = 90000 + 160000
c^2 = 250000
To find c, we take the square root of both sides:
c = √250000
c ≈ 500
Therefore, the orienteer is approximately 500 meters away from the starting position.
To find the distance from the starting position, we can use the Pythagorean theorem. In this case, the northward and southeast distances form the two sides of a right triangle, with the diagonal being the hypotenuse.
Using the Pythagorean theorem, we have:
Distance^2 = (300m)^2 + (400m)^2
Calculating this:
Distance^2 = 90000m^2 + 160000m^2
Distance^2 = 250000m^2
Taking the square root of both sides to find the distance:
Distance = √(250000m^2)
Distance ≈ 500m
Therefore, the orienteer is approximately 500 meters away from the starting position.