Question
For the values a = 2.9 which is a leg of a right triangle, and value c = 4.2, which is the hypotenuse, find the length of the other leg, b, to the nearest tenth.
2.8
3.0
2.9
1.3
2.8
3.0
2.9
1.3
Answers
GPT-4o mini
To find the length of the other leg \( b \) of a right triangle given one leg \( a \) and the hypotenuse \( c \), we can use the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
We are given:
- \( a = 2.9 \)
- \( c = 4.2 \)
Now we can substitute these values into the equation and solve for \( b \):
1. Calculate \( a^2 \):
\[
a^2 = (2.9)^2 = 8.41
\]
2. Calculate \( c^2 \):
\[
c^2 = (4.2)^2 = 17.64
\]
3. Substitute \( a^2 \) and \( c^2 \) back into the equation:
\[
8.41 + b^2 = 17.64
\]
4. Rearranging the equation to solve for \( b^2 \):
\[
b^2 = 17.64 - 8.41 = 9.23
\]
5. Finally, take the square root of \( b^2 \) to find \( b \):
\[
b = \sqrt{9.23} \approx 3.0
\]
So, the length of the other leg \( b \) is approximately \( 3.0 \) when rounded to the nearest tenth.
Therefore, the answer is \( \boxed{3.0} \).
\[
a^2 + b^2 = c^2
\]
We are given:
- \( a = 2.9 \)
- \( c = 4.2 \)
Now we can substitute these values into the equation and solve for \( b \):
1. Calculate \( a^2 \):
\[
a^2 = (2.9)^2 = 8.41
\]
2. Calculate \( c^2 \):
\[
c^2 = (4.2)^2 = 17.64
\]
3. Substitute \( a^2 \) and \( c^2 \) back into the equation:
\[
8.41 + b^2 = 17.64
\]
4. Rearranging the equation to solve for \( b^2 \):
\[
b^2 = 17.64 - 8.41 = 9.23
\]
5. Finally, take the square root of \( b^2 \) to find \( b \):
\[
b = \sqrt{9.23} \approx 3.0
\]
So, the length of the other leg \( b \) is approximately \( 3.0 \) when rounded to the nearest tenth.
Therefore, the answer is \( \boxed{3.0} \).