Find the length of the hypotenuse, side C, , of a right triangle with legs of length A=6 and B=12. Use a calculator to estimate the square root to one decimal place.
Question
Find the length of the hypotenuse, side C, , of a right triangle with legs of length A=6 and B=12.
Use a calculator to estimate the square root to one decimal place.
Solution
To find the length of the hypotenuse (side C) of a right triangle, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the lengths of the other two sides are given as A=6 and B=12.
Here are the steps to solve the problem:
- Square the lengths of the two sides: A^2 = 6^2 = 36 and B^2 = 12^2 = 144.
- Add these two values together: A^2 + B^2 = 36 + 144 = 180.
- Take the square root of this sum to find the length of the hypotenuse: C = sqrt(180).
Using a calculator, the square root of 180 is approximately 13.4 (to one decimal place). So, the length of the hypotenuse, side C, is approximately 13.4 units.
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