sarah sailed 12 miles due south from a buoy. Then she sailed 11 miles due west. How far was she from the buoy. estimate to the nearest 10th.
a^2 + b^2 = c^2
12^2 + 11^2 = c^2
144 + 121 = c^2
265 = c^2
16.3 = c
To determine how far Sarah was from the buoy, we can use the Pythagorean theorem, which 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 distance Sarah sailed south forms one side of a right triangle, and the distance she sailed west forms the other side. The distance she is from the buoy (the hypotenuse) can be calculated using the formula:
distance from the buoy^2 = (distance sailed south)^2 + (distance sailed west)^2
Let's calculate it step-by-step:
1. Sarah sailed 12 miles due south from the buoy. This forms one side of the right triangle, so the distance sailed south is 12 miles.
2. Sarah then sailed 11 miles due west. This forms the other side of the right triangle, so the distance sailed west is 11 miles.
3. Substitute the values into the formula:
(distance from the buoy)^2 = (12 miles)^2 + (11 miles)^2
4. Calculate:
(distance from the buoy)^2 = 144 + 121
(distance from the buoy)^2 = 265
5. Take the square root of both sides to find the distance from the buoy:
distance from the buoy ≈ √265
distance from the buoy ≈ 16.28
Rounding to the nearest tenth, Sarah was approximately 16.3 miles from the buoy.