Question
Finding the missing side of the right triangle. Round your answer to the nearest tenth.
we have 27 and 9
we have 27 and 9
Answers
GPT-4o mini
To find the missing side of a right triangle, we can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
Where \( c \) is the length of the hypotenuse (the longest side), and \( a \) and \( b \) are the lengths of the other two sides.
From your statement, it seems you may have two sides (27 and 9). We need to determine which one is the hypotenuse.
1. **Assuming 27 is the hypotenuse**:
\[
9^2 + b^2 = 27^2
\]
\[
81 + b^2 = 729
\]
\[
b^2 = 729 - 81
\]
\[
b^2 = 648
\]
\[
b = \sqrt{648} \approx 25.5
\]
2. **Assuming 9 is one of the legs** and 27 is the hypotenuse:
\[
a^2 + 9^2 = 27^2
\]
\[
a^2 + 81 = 729
\]
\[
a^2 = 729 - 81
\]
\[
a^2 = 648
\]
\[
a = \sqrt{648} \approx 25.5
\]
In both cases, the missing side (the other leg) is approximately 25.5.
Hence, rounding to the nearest tenth, the length of the missing side is **25.5**.
\[
a^2 + b^2 = c^2
\]
Where \( c \) is the length of the hypotenuse (the longest side), and \( a \) and \( b \) are the lengths of the other two sides.
From your statement, it seems you may have two sides (27 and 9). We need to determine which one is the hypotenuse.
1. **Assuming 27 is the hypotenuse**:
\[
9^2 + b^2 = 27^2
\]
\[
81 + b^2 = 729
\]
\[
b^2 = 729 - 81
\]
\[
b^2 = 648
\]
\[
b = \sqrt{648} \approx 25.5
\]
2. **Assuming 9 is one of the legs** and 27 is the hypotenuse:
\[
a^2 + 9^2 = 27^2
\]
\[
a^2 + 81 = 729
\]
\[
a^2 = 729 - 81
\]
\[
a^2 = 648
\]
\[
a = \sqrt{648} \approx 25.5
\]
In both cases, the missing side (the other leg) is approximately 25.5.
Hence, rounding to the nearest tenth, the length of the missing side is **25.5**.