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
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
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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.