Question
What is the length of the missing leg? One leg is 3 mm and the slope is 7 mm. If necessary, round to the nearest tenth.
Answers
GPT-4o mini
To find the length of the missing leg in a right triangle, we can use the Pythagorean theorem, which states that:
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse (the slope in this case).
In your case:
- One leg (\( a \)) = 3 mm
- The hypotenuse (\( c \)) = 7 mm
We need to find the length of the other leg (\( b \)).
Plugging in the known values into the Pythagorean theorem:
\[
3^2 + b^2 = 7^2
\]
Calculating the squares:
\[
9 + b^2 = 49
\]
Now, isolate \( b^2 \):
\[
b^2 = 49 - 9
\]
\[
b^2 = 40
\]
Now take the square root of both sides to find \( b \):
\[
b = \sqrt{40}
\]
Calculating \( \sqrt{40} \):
\[
b \approx 6.3246
\]
Rounding to the nearest tenth:
\[
b \approx 6.3 \text{ mm}
\]
Thus, the length of the missing leg is approximately **6.3 mm**.
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse (the slope in this case).
In your case:
- One leg (\( a \)) = 3 mm
- The hypotenuse (\( c \)) = 7 mm
We need to find the length of the other leg (\( b \)).
Plugging in the known values into the Pythagorean theorem:
\[
3^2 + b^2 = 7^2
\]
Calculating the squares:
\[
9 + b^2 = 49
\]
Now, isolate \( b^2 \):
\[
b^2 = 49 - 9
\]
\[
b^2 = 40
\]
Now take the square root of both sides to find \( b \):
\[
b = \sqrt{40}
\]
Calculating \( \sqrt{40} \):
\[
b \approx 6.3246
\]
Rounding to the nearest tenth:
\[
b \approx 6.3 \text{ mm}
\]
Thus, the length of the missing leg is approximately **6.3 mm**.