Question

On the third day of camp, you go canoeing on the camp lake. You paddle from the dock due north for 500 yards and then due west for 475 yards. How far are you from the dock?

Answer 1

The distance from the dock after canoeing north for 500 yards and then west for 475 yards is approximately 689.06 yards.

Step-by-step explanation:

To calculate the distance from the dock after canoeing north for 500 yards and then west for 475 yards, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square 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 north and west distances are the two sides of the right triangle and the distance from the dock is the hypotenuse.

The distance from the dock can be calculated as follows:

a^2 + b^2 = c^2

Where a and b are the north and west distances respectively, and c is the distance from the dock.

Plugging in the values, we have:

500^2 + 475^2 = c^2

Solving for c:

250000 + 225625 = c^2

475625 = c^2

c ≈ 689.06 yards

So, the distance from the dock is approximately 689.06 yards.