In diving to a depth of 979 m, an elephant seal also moves 104 m due east of his starting point. What is the magnitude of the seal's displacement?
Isn't this a right triangle?
To find the magnitude of the seal's displacement, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the seal's displacement can be represented by a right-angled triangle, with one side measuring 979 m (depth) and the other side measuring 104 m (eastward movement). Let's call the magnitude of the displacement "d".
Using the Pythagorean theorem, we can set up the equation as follows:
d^2 = 979^2 + 104^2
To solve for "d," we need to calculate the values on the right-hand side of the equation:
979^2 = 958,441
104^2 = 10,816
Now, we can substitute these values back into the equation:
d^2 = 958,441 + 10,816
Simplifying:
d^2 = 969,257
To find the value of "d," we need to take the square root of both sides of the equation:
d = √969,257
Using a calculator or computing software, we can find that the square root of 969,257 is approximately 984.5.
Therefore, the magnitude of the seal's displacement is approximately 984.5 meters.