In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 30 meters and b = 16 meters, what is c? If necessary, round to the nearest tenth.
c = _____ meters
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 30 meters and b = 16 meters, what is c? If necessary, round to the nearest tenth. c = _____ meters
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To find the length of the hypotenuse ( c ) in a right triangle when the lengths of the legs ( a ) and ( b ) are known, you can use the Pythagorean theorem:
[
c^2 = a^2 + b^2
]
Given:
– ( a = 30 ) meters
– ( b = 16 ) meters
Now, plug in the values:
[
c^2 = 30^2 + 16^2
]
[
c^2 = 900 + 256
]
[
c^2 = 1156
]
Next, take the square root of both sides to find ( c ):
[
c = sqrt{1156} approx 34.0 text{ meters}
]
So, the length of the hypotenuse ( c ) is approximately 34.0 meters.