Question
Find the missing side of the right triangle. Round your answer to the nearest tenth. The base is 8 and the diagonal is 32
Answers
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Answered by
GPT-4o mini
To find the missing side of a right triangle, we can use the Pythagorean theorem, which is given by:
\[
a^2 + b^2 = c^2
\]
where \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse.
In this case, the base (one leg) \(a\) is 8, and the diagonal (hypotenuse) \(c\) is 32. We are trying to find the other leg \(b\).
Plugging the values into the Pythagorean theorem:
\[
8^2 + b^2 = 32^2
\]
Calculating the squares:
\[
64 + b^2 = 1024
\]
Now, we can isolate \(b^2\):
\[
b^2 = 1024 - 64
\]
\[
b^2 = 960
\]
Next, we take the square root of both sides to find \(b\):
\[
b = \sqrt{960}
\]
Calculating the square root:
\[
b \approx 31.0
\]
Therefore, the missing side \(b\) rounded to the nearest tenth is approximately **31.0**.
\[
a^2 + b^2 = c^2
\]
where \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse.
In this case, the base (one leg) \(a\) is 8, and the diagonal (hypotenuse) \(c\) is 32. We are trying to find the other leg \(b\).
Plugging the values into the Pythagorean theorem:
\[
8^2 + b^2 = 32^2
\]
Calculating the squares:
\[
64 + b^2 = 1024
\]
Now, we can isolate \(b^2\):
\[
b^2 = 1024 - 64
\]
\[
b^2 = 960
\]
Next, we take the square root of both sides to find \(b\):
\[
b = \sqrt{960}
\]
Calculating the square root:
\[
b \approx 31.0
\]
Therefore, the missing side \(b\) rounded to the nearest tenth is approximately **31.0**.
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