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

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.

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 ]

where (a) and (b) are the lengths of the legs. Given (a = 30) meters and (b = 16) meters, we can plug in these values:

1. Calculate (a^2) and (b^2):

– (a^2 = 30^2 = 900)

– (b^2 = 16^2 = 256)

2. Add these values together:

– (c^2 = 900 + 256 = 1156)

3. Now, take the square root to find (c):

– (c = sqrt{1156} = 34)

So, the length of the hypotenuse (c) is approximately 34.0 meters when rounded to the nearest tenth.

c = 34.0 meters