Calculating the Length of the Third Leg in a Right Triangle
The image shows a right triangle with one leg of length 7, the hypotenuse of length 9, and the other leg (which we want to find) labeled 'x'.
To solve for 'x', we can use the Pythagorean theorem, which states that for a right triangle with legs 'a' and 'b', and hypotenuse 'c', the following equation holds true:
a² + b² = c²
Here, 'a' is 7, 'b' is 'x', and 'c' is 9. Plugging in the values we have:
7² + x² = 9²
49 + x² = 81
Now we'll solve for x²:
x² = 81 - 49
x² = 32
Taking the square root of both sides to solve for 'x':
x = √32
Now we can calculate the value of 'x' and round it to the nearest tenth:
x ≈ 5.7
So, 'x' rounded to the nearest tenth is approximately 5.7.
