Question
T. 1 Pythagorean theorem: find the length of the hypotenuse InL If \( a=7 \) meters and \( b=3 \) meters, what is \( c \) ? If necessary, round to the nearest tenth. \( c= \) Submit
Ask by Flynn Willis. in the United States
Mar 06,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The length of the hypotenuse \( c \) is approximately 7.6 meters.
Solution
To find the length of the hypotenuse \( c \) using the Pythagorean theorem, we can use the formula:
\[ c^2 = a^2 + b^2 \]
Given:
- \( a = 7 \) meters
- \( b = 3 \) meters
Substitute the values of \( a \) and \( b \) into the formula:
\[ c^2 = 7^2 + 3^2 \]
\[ c^2 = 49 + 9 \]
\[ c^2 = 58 \]
Now, we need to find the square root of 58 to get the value of \( c \):
\[ c = \sqrt{58} \]
Let's calculate the value of \( c \) and round it to the nearest tenth.
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{58}\)
The length of the hypotenuse \( c \) is approximately 7.6 meters when rounded to the nearest tenth.
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Simplify this solution Beyond the Answer
To find the length of the hypotenuse \( c \) using the Pythagorean theorem, we use the formula \( c = \sqrt{a^2 + b^2} \). Plugging in the values, we get \( c = \sqrt{7^2 + 3^2} = \sqrt{49 + 9} = \sqrt{58} \). When calculated, \( c \approx 7.6 \) meters when rounded to the nearest tenth. So, \( c \approx 7.6 \) meters! Keep this handy for when you're figuring out the dimensions of a geometric triangle or when setting up the perfect pitch for your treehouse!
