Question
A right triangle has a leg measuring 34 yards a side leg measuring 16 yards. what is the length of the missing leg. Round to the nearest tenth if necessary
Answers
GPT-4o mini
In a right triangle, you can use the Pythagorean theorem to find the length of the missing side. The theorem states that:
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two legs.
Given:
- One leg \(a = 34\) yards
- The other leg \(b = 16\) yards
To find the missing leg \(c\) (the length of the hypotenuse), we rearrange the formula as follows:
\[
c = \sqrt{a^2 + b^2}
\]
Now, plug in the values of \(a\) and \(b\):
\[
c = \sqrt{34^2 + 16^2}
\]
Calculating the squares:
\[
34^2 = 1156
\]
\[
16^2 = 256
\]
Adding these:
\[
c = \sqrt{1156 + 256} = \sqrt{1412}
\]
Now, calculate the square root:
\[
c \approx 37.5
\]
So, the length of the hypotenuse (the missing leg) is approximately **37.5 yards**.
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two legs.
Given:
- One leg \(a = 34\) yards
- The other leg \(b = 16\) yards
To find the missing leg \(c\) (the length of the hypotenuse), we rearrange the formula as follows:
\[
c = \sqrt{a^2 + b^2}
\]
Now, plug in the values of \(a\) and \(b\):
\[
c = \sqrt{34^2 + 16^2}
\]
Calculating the squares:
\[
34^2 = 1156
\]
\[
16^2 = 256
\]
Adding these:
\[
c = \sqrt{1156 + 256} = \sqrt{1412}
\]
Now, calculate the square root:
\[
c \approx 37.5
\]
So, the length of the hypotenuse (the missing leg) is approximately **37.5 yards**.