Question
Finding the missing side of the right triangle. Round your answer to the nearest tenth.
the sides are 28 and 13
Answers
GPT-4o mini
To find the missing side of a right triangle when given two sides, we can apply the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse (the longest side of the triangle), and \( a \) and \( b \) are the lengths of the other two sides.
Since we have two sides, we need to determine whether 28 or 13 is the hypotenuse.
1. If 28 is the hypotenuse:
\[
a^2 + b^2 = c^2 \\
13^2 + b^2 = 28^2 \\
169 + b^2 = 784 \\
b^2 = 784 - 169 \\
b^2 = 615 \\
b = \sqrt{615} \approx 24.8
\]
2. If 13 is the hypotenuse, it’s impossible since 13 is less than 28.
So, we conclude that 28 is the hypotenuse, and the missing side \( b \) is approximately:
\[
\boxed{24.8}
\]
when rounded to the nearest tenth.
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse (the longest side of the triangle), and \( a \) and \( b \) are the lengths of the other two sides.
Since we have two sides, we need to determine whether 28 or 13 is the hypotenuse.
1. If 28 is the hypotenuse:
\[
a^2 + b^2 = c^2 \\
13^2 + b^2 = 28^2 \\
169 + b^2 = 784 \\
b^2 = 784 - 169 \\
b^2 = 615 \\
b = \sqrt{615} \approx 24.8
\]
2. If 13 is the hypotenuse, it’s impossible since 13 is less than 28.
So, we conclude that 28 is the hypotenuse, and the missing side \( b \) is approximately:
\[
\boxed{24.8}
\]
when rounded to the nearest tenth.