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!
Answers
Answered by
GPT-4o mini
To find the length of the other leg of a right triangle given one leg and the hypotenuse, we can use the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the lengths of the legs and \( c \) is the length of the hypotenuse. In this case, we have one leg \( a = 12 \) in and the hypotenuse \( c = 16 \) in. We need to find the length of the other leg \( b \).
First, we rearrange the equation to solve for \( b \):
\[
b^2 = c^2 - a^2
\]
Now substituting in the known values:
\[
b^2 = 16^2 - 12^2
\]
Calculating \( 16^2 \) and \( 12^2 \):
\[
16^2 = 256
\]
\[
12^2 = 144
\]
Now substitute these values into the equation:
\[
b^2 = 256 - 144
\]
\[
b^2 = 112
\]
Next, we take the square root of both sides to find \( b \):
\[
b = \sqrt{112}
\]
Calculating \( \sqrt{112} \):
\[
\sqrt{112} \approx 10.583
\]
Thus, the length of the other leg is approximately \( 10.58 \) inches.
So the final answer is:
**Approximately 10.58 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 have one leg \( a = 12 \) in and the hypotenuse \( c = 16 \) in. We need to find the length of the other leg \( b \).
First, we rearrange the equation to solve for \( b \):
\[
b^2 = c^2 - a^2
\]
Now substituting in the known values:
\[
b^2 = 16^2 - 12^2
\]
Calculating \( 16^2 \) and \( 12^2 \):
\[
16^2 = 256
\]
\[
12^2 = 144
\]
Now substitute these values into the equation:
\[
b^2 = 256 - 144
\]
\[
b^2 = 112
\]
Next, we take the square root of both sides to find \( b \):
\[
b = \sqrt{112}
\]
Calculating \( \sqrt{112} \):
\[
\sqrt{112} \approx 10.583
\]
Thus, the length of the other leg is approximately \( 10.58 \) inches.
So the final answer is:
**Approximately 10.58 in.**