In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 9 feet and c = 10 feet, what is b? If necessary, round to the nearest tenth. b = ____ feet

To find the length of the leg ( b ) in a right triangle, we can use the Pythagorean theorem, which states that ( a^2 + b^2 = c^2 ).

Given:

– ( a = 9 ) feet

– ( c = 10 ) feet

We can rearrange the formula to solve for ( b ):

[

b^2 = c^2 – a^2

]

Now, let’s plug in the values:

[

b^2 = 10^2 – 9^2

]

[

b^2 = 100 – 81

]

[

b^2 = 19

]

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

[

b = sqrt{19} approx 4.4 text{ feet}

]

Thus, the length of ( b ) is approximately 4.4 feet.