Question
Find the missing lengths. Round to the nearest tenth.
The hypotenuse of the right triangle is seven while the shorter leg is four. What's the longer leg?
The hypotenuse of the right triangle is seven while the shorter leg is four. What's the longer leg?
Answers
GPT-4o mini
To find the length of the longer leg in a right triangle, we can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse.
In this triangle, we have:
- Hypotenuse \( c = 7 \)
- Shorter leg \( a = 4 \)
- Longer leg \( b = ? \)
Substituting the values into the theorem, we have:
\[
4^2 + b^2 = 7^2
\]
Calculating the squares:
\[
16 + b^2 = 49
\]
Next, we solve for \( b^2 \):
\[
b^2 = 49 - 16
\]
\[
b^2 = 33
\]
Now, we take the square root to find \( b \):
\[
b = \sqrt{33} \approx 5.744
\]
Rounding to the nearest tenth:
\[
b \approx 5.7
\]
Thus, the length of the longer leg is approximately **5.7**.
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse.
In this triangle, we have:
- Hypotenuse \( c = 7 \)
- Shorter leg \( a = 4 \)
- Longer leg \( b = ? \)
Substituting the values into the theorem, we have:
\[
4^2 + b^2 = 7^2
\]
Calculating the squares:
\[
16 + b^2 = 49
\]
Next, we solve for \( b^2 \):
\[
b^2 = 49 - 16
\]
\[
b^2 = 33
\]
Now, we take the square root to find \( b \):
\[
b = \sqrt{33} \approx 5.744
\]
Rounding to the nearest tenth:
\[
b \approx 5.7
\]
Thus, the length of the longer leg is approximately **5.7**.