Question
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=
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Answered by
GPT-4o mini
To find the length of the hypotenuse \( c \) of a right triangle given the lengths of the other two legs \( a \) and \( b \), you can use the Pythagorean theorem, which states:
\[
c^2 = a^2 + b^2
\]
Given:
- \( a = 30 \) meters
- \( b = 16 \) meters
Now, we can plug in the values:
\[
c^2 = 30^2 + 16^2
\]
\[
c^2 = 900 + 256
\]
\[
c^2 = 1156
\]
Now, take the square root of both sides to find \( c \):
\[
c = \sqrt{1156}
\]
Calculating the square root:
\[
c \approx 34.0 \text{ meters}
\]
Thus, the length of the hypotenuse \( c \) is approximately \( \boxed{34.0} \) meters.
\[
c^2 = a^2 + b^2
\]
Given:
- \( a = 30 \) meters
- \( b = 16 \) meters
Now, we can plug in the values:
\[
c^2 = 30^2 + 16^2
\]
\[
c^2 = 900 + 256
\]
\[
c^2 = 1156
\]
Now, take the square root of both sides to find \( c \):
\[
c = \sqrt{1156}
\]
Calculating the square root:
\[
c \approx 34.0 \text{ meters}
\]
Thus, the length of the hypotenuse \( c \) is approximately \( \boxed{34.0} \) meters.
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