Question
(1 point) If a right triangle has a leg with length 12 in. and the hypotenuse is 16 in., the other leg must be approximately in.. Hint: Don't forget to use your Desmos calculator and STAAR Reference Sheet to help!
answer choices are
11.5
10.6
20
8.6
answer choices are
11.5
10.6
20
8.6
Answers
Answered by
GPT-4o mini
To find the length of the other leg in a right triangle where one leg is 12 inches and the hypotenuse is 16 inches, 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 case, we can denote the known leg as \(a = 12\) in, the unknown leg as \(b\), and the hypotenuse as \(c = 16\) in. Substituting the known values into the equation:
\[
12^2 + b^2 = 16^2
\]
Calculating the squares:
\[
144 + b^2 = 256
\]
Now, we subtract 144 from both sides:
\[
b^2 = 256 - 144
\]
\[
b^2 = 112
\]
Next, we take the square root of both sides to find \(b\):
\[
b = \sqrt{112}
\]
Calculating \(\sqrt{112}\):
\[
b \approx 10.58
\]
Rounding this value, we can approximate it as 10.6.
Thus, the length of the other leg is approximately **10.6 in.**
\[
a^2 + b^2 = c^2
\]
where \(a\) and \(b\) are the lengths of the legs, and \(c\) is the length of the hypotenuse.
In this case, we can denote the known leg as \(a = 12\) in, the unknown leg as \(b\), and the hypotenuse as \(c = 16\) in. Substituting the known values into the equation:
\[
12^2 + b^2 = 16^2
\]
Calculating the squares:
\[
144 + b^2 = 256
\]
Now, we subtract 144 from both sides:
\[
b^2 = 256 - 144
\]
\[
b^2 = 112
\]
Next, we take the square root of both sides to find \(b\):
\[
b = \sqrt{112}
\]
Calculating \(\sqrt{112}\):
\[
b \approx 10.58
\]
Rounding this value, we can approximate it as 10.6.
Thus, the length of the other leg is approximately **10.6 in.**