In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 2 kilometers and b = 5 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 when you have the lengths of the legs ( a ) and ( b ), you can use the Pythagorean theorem:

[

c^2 = a^2 + b^2

]

Given:

– ( a = 2 ) kilometers

– ( b = 5 ) kilometers

Now plug in the values:

[

c^2 = (2)^2 + (5)^2

]

[

c^2 = 4 + 25

]

[

c^2 = 29

]

Now take the square root of both sides to find ( c ):

[

c = sqrt{29} approx 5.385

]

Rounding to the nearest tenth:

[

c approx 5.4 text{ kilometers}

]

So, the answer is:

c = 5.4 kilometers

To find the length of the hypotenuse (c) in a right triangle, we can use the Pythagorean theorem, which states:

[ c^2 = a^2 + b^2 ]

Given:

– ( a = 2 ) kilometers

– ( b = 5 ) kilometers

Now, plug the values into the formula:

1. Square both a and b:

– ( a^2 = 2^2 = 4 )

– ( b^2 = 5^2 = 25 )

2. Add those squares together:

– ( c^2 = 4 + 25 = 29 )

3. Now take the square root to find c:

– ( c = sqrt{29} )

Using a calculator:

– ( c approx 5.385 )

Rounding to the nearest tenth gives:

– ( c approx 5.4 ) kilometers.

So, the final answer is:

c = 5.4 kilometers.