Question
the length of one of the legs in a right triangle is 14 inches the hypotenuse is 20 inches long what is the length of the other leg
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Answer
the answer is either 2checkmark51 or 2 checkmark 17
Answered by
GPT-4o mini
To find the length of the other leg of a right triangle, you can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two legs.
In this case, you have one leg (\( a \)) that is 14 inches and the hypotenuse (\( c \)) that is 20 inches. Let’s denote the length of the other leg as \( b \).
Plugging in the values we have:
\[
14^2 + b^2 = 20^2
\]
Calculating the squares:
\[
196 + b^2 = 400
\]
Now, subtract 196 from both sides:
\[
b^2 = 400 - 196
\]
\[
b^2 = 204
\]
Now, take the square root of both sides to find \( b \):
\[
b = \sqrt{204} \approx 14.28 \text{ inches}
\]
Therefore, the length of the other leg is approximately \( 14.28 \) inches.
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two legs.
In this case, you have one leg (\( a \)) that is 14 inches and the hypotenuse (\( c \)) that is 20 inches. Let’s denote the length of the other leg as \( b \).
Plugging in the values we have:
\[
14^2 + b^2 = 20^2
\]
Calculating the squares:
\[
196 + b^2 = 400
\]
Now, subtract 196 from both sides:
\[
b^2 = 400 - 196
\]
\[
b^2 = 204
\]
Now, take the square root of both sides to find \( b \):
\[
b = \sqrt{204} \approx 14.28 \text{ inches}
\]
Therefore, the length of the other leg is approximately \( 14.28 \) inches.
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