A right triangle has legs 11 and 14. Find the hypotenuse
视频信息
答案文本
视频字幕
We are given a right triangle with legs of length 11 and 14 units. Our goal is to find the length of the hypotenuse, which is the longest side opposite the right angle.
The key to solving this problem is the Pythagorean theorem. This fundamental principle states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, known as the legs.
Now we'll substitute our known values into the Pythagorean theorem. We have a equals 11 and b equals 14, so our equation becomes 11 squared plus 14 squared equals c squared.
Next, we calculate the squares of our leg lengths. Eleven squared is 121, and fourteen squared is 196. So our equation now becomes 121 plus 196 equals c squared.
Adding 121 and 196 gives us 317. Therefore, c squared equals 317. To find c, we need to take the square root of both sides.
Taking the square root of both sides, we find that c equals the square root of 317. Using a calculator, we determine that the square root of 317 is approximately 17.80 units.
To summarize our solution: We started with a right triangle with legs of 11 and 14 units. We applied the Pythagorean theorem, substituted our values, calculated the squares, added them to get 317, and took the square root to find that the hypotenuse is approximately 17.80 units. This method works for any right triangle when two sides are known.