The hypotenuse of a right triangle is √23 in and one leg measures 4 in. Find the length of the other leg.

Question

The hypotenuse of a right triangle is √23 in and one leg measures 4 in. Find the length of the other leg.

What is the exact length of the other​ leg? ______ in

Answer 1

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 a² + b² = c².

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: 4² + x² = (√23)².

4² = 16, and (√23)² is just 23, so if you substitute these values in and subtract 16 from both sides, you get x² = 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.

Answer 2

a²+b²=c²

4²+b²⁼23

16+b²=23

b²=7

b=√7