Question
Use Pythagorean Theorem to find the missing length of a leg? (1 point) Responses 17.5 17.5 144 144 12 12 225 ( One side is 15, the other is 9)
Answers
GPT-4o mini
To find the missing length of a leg in a right triangle using the Pythagorean Theorem, we use the formula:
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case, one leg is 15, and the other leg is 9. We can find the length of the hypotenuse \( c \) first:
\[
15^2 + 9^2 = c^2
\]
Calculating the squares:
\[
15^2 = 225
\]
\[
9^2 = 81
\]
Now, add these values together:
\[
225 + 81 = c^2
\]
\[
306 = c^2
\]
Now, to find the length of the hypotenuse \( c \):
\[
c = \sqrt{306} \approx 17.44
\]
Now, if you want to find a missing leg given the hypotenuse and one leg, we rearrange the formula to solve for the missing leg, say \( b \):
\[
b^2 = c^2 - a^2
\]
If suppose we need to find a leg with a hypotenuse of 15 and the other leg of 9:
\[
b^2 = 15^2 - 9^2
\]
\[
b^2 = 225 - 81
\]
\[
b^2 = 144
\]
\[
b = \sqrt{144} = 12
\]
So, the missing leg length is \( 12 \). The answer is **12**.
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case, one leg is 15, and the other leg is 9. We can find the length of the hypotenuse \( c \) first:
\[
15^2 + 9^2 = c^2
\]
Calculating the squares:
\[
15^2 = 225
\]
\[
9^2 = 81
\]
Now, add these values together:
\[
225 + 81 = c^2
\]
\[
306 = c^2
\]
Now, to find the length of the hypotenuse \( c \):
\[
c = \sqrt{306} \approx 17.44
\]
Now, if you want to find a missing leg given the hypotenuse and one leg, we rearrange the formula to solve for the missing leg, say \( b \):
\[
b^2 = c^2 - a^2
\]
If suppose we need to find a leg with a hypotenuse of 15 and the other leg of 9:
\[
b^2 = 15^2 - 9^2
\]
\[
b^2 = 225 - 81
\]
\[
b^2 = 144
\]
\[
b = \sqrt{144} = 12
\]
So, the missing leg length is \( 12 \). The answer is **12**.