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
Share
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