Question
What is the length of the missing leg? One of the legs are 16 yd and the slope is 20 yd. If necessary, round to the nearest tenth.
Answers
GPT-4o mini
To find the length of the missing leg of a right triangle when given one leg and the hypotenuse (slope), we can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse.
In your case, let:
- \( a = 16 \) yd (one leg)
- \( c = 20 \) yd (hypotenuse)
- \( b \) = missing leg
We can rearrange the Pythagorean theorem to solve for \( b \):
\[
b^2 = c^2 - a^2
\]
Substituting the values we have:
\[
b^2 = 20^2 - 16^2
\]
\[
b^2 = 400 - 256
\]
\[
b^2 = 144
\]
Now, take the square root of both sides to find \( b \):
\[
b = \sqrt{144} = 12 \text{ yd}
\]
Therefore, the length of the missing leg is **12 yards**.
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse.
In your case, let:
- \( a = 16 \) yd (one leg)
- \( c = 20 \) yd (hypotenuse)
- \( b \) = missing leg
We can rearrange the Pythagorean theorem to solve for \( b \):
\[
b^2 = c^2 - a^2
\]
Substituting the values we have:
\[
b^2 = 20^2 - 16^2
\]
\[
b^2 = 400 - 256
\]
\[
b^2 = 144
\]
Now, take the square root of both sides to find \( b \):
\[
b = \sqrt{144} = 12 \text{ yd}
\]
Therefore, the length of the missing leg is **12 yards**.