In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 4 inches and c = 7 inches, what is b? If necessary, round to the nearest tenth. b = _____ inches

To find the length of leg b in a right triangle when you know the lengths of both legs (a) and the hypotenuse (c), you can use the Pythagorean theorem, which states:

[ a^2 + b^2 = c^2 ]

Given:

– a = 4 inches

– c = 7 inches

Substituting the values into the equation:

[ 4^2 + b^2 = 7^2 ]

[ 16 + b^2 = 49 ]

Now, subtract 16 from both sides:

[ b^2 = 49 – 16 ]

[ b^2 = 33 ]

Next, take the square root of both sides to find b:

[ b = sqrt{33} ]

Calculating the value:

[ b approx 5.7 text{ inches} ]

So, the length of leg b is approximately 5.7 inches.