In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 3.4 kilometers and b = 1.8 kilometers, what is c? If necessary, round to the nearest tenth.
c = _____ kilometers
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 3.4 kilometers and b = 1.8 kilometers, what is c? If necessary, round to the nearest tenth. c = _____ kilometers.
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To find the length of the hypotenuse ( c ) in a right triangle, you can use the Pythagorean theorem, which states:
[
c^2 = a^2 + b^2
]
Given that ( a = 3.4 ) kilometers and ( b = 1.8 ) kilometers, plug in the values:
[
c^2 = (3.4)^2 + (1.8)^2
]
Calculating each term:
[
(3.4)^2 = 11.56
]
[
(1.8)^2 = 3.24
]
Now, add those results:
[
c^2 = 11.56 + 3.24 = 14.80
]
Next, take the square root to find ( c ):
[
c = sqrt{14.80} approx 3.85
]
Rounding to the nearest tenth gives:
[
c approx 3.9 text{ kilometers}
]
So, the length of the hypotenuse ( c ) is approximately 3.9 kilometers.