In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 44 meters and c = 55 meters, what is b? If necessary, round to the nearest tenth.
b = _____ meters
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 44 meters and c = 55 meters, what is b? If necessary, round to the nearest tenth. b equals _____ meters
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To find the length of leg ( b ) in a right triangle where the lengths of the legs are ( a ) and ( b ), and the hypotenuse is ( c ), we can use the Pythagorean theorem:
[
a^2 + b^2 = c^2
]
Given:
– ( a = 44 ) meters
– ( c = 55 ) meters
We can substitute the values into the equation:
[
44^2 + b^2 = 55^2
]
Calculating the squares:
[
1936 + b^2 = 3025
]
Now, subtract ( 1936 ) from both sides:
[
b^2 = 3025 – 1936
]
[
b^2 = 1089
]
Now, take the square root of both sides:
[
b = sqrt{1089} approx 33
]
So, the length of leg ( b ) is approximately ( 33.0 ) meters.
b = 33.0 meters