In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 6.7 feet and c = 10 feet, what is b? If necessary, round to the nearest tenth. b = _____ feet

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

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

Given that ( a = 6.7 ) feet and ( c = 10 ) feet, you can plug in these values:

1. Calculate ( a^2 ):

[ a^2 = (6.7)^2 = 44.89 ]

2. Calculate ( c^2 ):

[ c^2 = (10)^2 = 100 ]

3. Now, substitute these into the Pythagorean theorem:

[ 44.89 + b^2 = 100 ]

4. Rearranging gives:

[ b^2 = 100 – 44.89 ]

[ b^2 = 55.11 ]

5. Take the square root of both sides to find b:

[ b = sqrt{55.11} ]

[ b approx 7.4 , text{feet} ] (rounded to the nearest tenth)

So, the length of leg b is approximately 7.4 feet.