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, we can use the Pythagorean theorem, which states:

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

Given that:

– ( a = 4 ) inches

– ( c = 7 ) inches

We can rearrange the formula to find b:

1. Substitute the values into the equation:

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

[ 16 + b^2 = 49 ]

2. Subtract 16 from both sides:

[ b^2 = 49 – 16 ]

[ b^2 = 33 ]

3. Take the square root of both sides:

[ b = sqrt{33} ]

4. To round to the nearest tenth:

[ b approx 5.7 ] inches

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