A submarine travels 13 km due East from its base and then turns and travels due North for 6.7 km.
How far away is the submarine from its base?
Use the Pythagorean Theorem.
a^2 + b^2 = c^2
13^2 + 6.7^2 = c^2
To find the distance between the submarine and its base, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 other two sides.
In this case, the submarine has traveled 13 km due East and then turned and traveled 6.7 km due North. These two distances form the two sides of a right-angled triangle, where the hypotenuse represents the straight-line distance between the submarine and its base.
Let's denote the distance traveled due East as "x" and the distance traveled due North as "y". We can use the Pythagorean theorem to solve for the hypotenuse:
Hypotenuse^2 = x^2 + y^2
Plugging in the given values:
Hypotenuse^2 = (13 km)^2 + (6.7 km)^2
Hypotenuse^2 = 169 km^2 + 44.89 km^2
Hypotenuse^2 = 213.89 km^2
To find the hypotenuse, we take the square root of both sides:
Hypotenuse = √(213.89 km^2)
Hypotenuse ≈ 14.62 km
Therefore, the submarine is approximately 14.62 km away from its base.