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.

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.