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 leg is 15, the other is 9)

Answer 1

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 two legs.

In your example, we have one leg \( a = 15 \) and another leg \( b = 9 \). We need to find the hypotenuse \( c \):

\[
c^2 = a^2 + b^2
\]
\[
c^2 = 15^2 + 9^2
\]
\[
c^2 = 225 + 81
\]
\[
c^2 = 306
\]
\[
c = \sqrt{306} \approx 17.5
\]

So the missing length of the hypotenuse is approximately 17.5.

If the intention was to find one of the legs given the hypotenuse and the other leg, let’s clarify that:
If one leg is 15 and the hypotenuse is unknown but equal to 17.5, and one leg is 9, we can find the missing leg \( b \):

\[
15^2 + b^2 = 17.5^2
\]
\[
225 + b^2 = 306.25
\]
\[
b^2 = 306.25 - 225
\]
\[
b^2 = 81.25
\]
\[
b \approx \sqrt{81.25} \approx 9.01
\]

However, based on your inquiry, it appears likely that you are looking at the length 17.5, which fits the hypotenuse derived from the legs provided.