Gaurav P. answered • 07/28/20

Computer Science Student with Teaching Experience

The Pythagorean theorem states the relationship between a right triangle's legs and its hypotenuse: if the legs' lengths are a and b and the hypotenuse's length is c, then a^{2} + b^{2} = c^{2}.

In your question, we have a right triangle with one leg 4 inches long, the other leg an unknown x inches long, and the hypotenuse √23 inches long, Substituting these into the formula, we get: 4^{2} + x^{2} = (√23)^{2}.

4^{2} = 16, and (√23)^{2} is just 23, so if you substitute these values in and subtract 16 from both sides, you get x^{2} = 23 - 16 = 7.

Taking the square root of both sides, we get x = √7. So our final answer is, the exact length of the other leg is **√7 inches**.