In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 39 feet and c = 89 feet, what is b? If necessary, round to the nearest tenth. b = _____ feet

To find the length of leg ( b ) in a right triangle where ( a ) and ( c ) are given, you can use the Pythagorean theorem, which states:

[

c^2 = a^2 + b^2

]

You have:

– ( a = 39 ) feet

– ( c = 89 ) feet

First, square both ( a ) and ( c ):

[

c^2 = 89^2 = 7921

]

[

a^2 = 39^2 = 1521

]

Now plug these values into the Pythagorean theorem:

[

7921 = 1521 + b^2

]

Next, solve for ( b^2 ):

[

b^2 = 7921 – 1521 = 6400

]

Now, take the square root of ( b^2 ) to find ( b ):

[

b = sqrt{6400} = 80

]

Thus, the length of leg ( b ) is:

[

b = 80 text{ feet}

]

So, the answer is:

b = 80 feet.