Question
find the length of the missing side for this right triangle. (estimate an irrational answer to two decimal places.)
a=3
b=?
c=5
a=3
b=?
c=5
Answers
Answered by
GPT-4o mini
In a right triangle, we can use the Pythagorean theorem, which states that \( a^2 + b^2 = c^2 \).
In this case, we know that:
- \( a = 3 \)
- \( c = 5 \)
- \( b \) is the missing side.
Plugging the known values into the Pythagorean equation:
\[
3^2 + b^2 = 5^2
\]
Calculating the squares:
\[
9 + b^2 = 25
\]
Now, isolate \( b^2 \):
\[
b^2 = 25 - 9
\]
\[
b^2 = 16
\]
Now, take the square root of both sides:
\[
b = \sqrt{16}
\]
Thus, we find:
\[
b = 4
\]
Therefore, the length of the missing side \( b \) is \( 4.00 \). If you need an irrational estimate or a decimal format, point out that \( 4 \) is not irrational; it is an exact integer, represented as \( 4.00 \).
In this case, we know that:
- \( a = 3 \)
- \( c = 5 \)
- \( b \) is the missing side.
Plugging the known values into the Pythagorean equation:
\[
3^2 + b^2 = 5^2
\]
Calculating the squares:
\[
9 + b^2 = 25
\]
Now, isolate \( b^2 \):
\[
b^2 = 25 - 9
\]
\[
b^2 = 16
\]
Now, take the square root of both sides:
\[
b = \sqrt{16}
\]
Thus, we find:
\[
b = 4
\]
Therefore, the length of the missing side \( b \) is \( 4.00 \). If you need an irrational estimate or a decimal format, point out that \( 4 \) is not irrational; it is an exact integer, represented as \( 4.00 \).