Question
length of the missing leg of a right triangle with one leg 5 inches and the hypotenuse 8 inches
Answers
Answered by
GPT-4o mini
To find the length of the missing leg of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle:
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the two legs. In this case, you have one leg \( a = 5 \) inches and the hypotenuse \( c = 8 \) inches. We need to find the other leg \( b \).
Plugging in the values we have:
\[
5^2 + b^2 = 8^2
\]
This simplifies to:
\[
25 + b^2 = 64
\]
To find \( b^2 \), we subtract 25 from both sides:
\[
b^2 = 64 - 25
\]
\[
b^2 = 39
\]
Now, taking the square root of both sides:
\[
b = \sqrt{39} \approx 6.24 \text{ inches}
\]
Thus, the length of the missing leg is approximately \( 6.24 \) inches.
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the two legs. In this case, you have one leg \( a = 5 \) inches and the hypotenuse \( c = 8 \) inches. We need to find the other leg \( b \).
Plugging in the values we have:
\[
5^2 + b^2 = 8^2
\]
This simplifies to:
\[
25 + b^2 = 64
\]
To find \( b^2 \), we subtract 25 from both sides:
\[
b^2 = 64 - 25
\]
\[
b^2 = 39
\]
Now, taking the square root of both sides:
\[
b = \sqrt{39} \approx 6.24 \text{ inches}
\]
Thus, the length of the missing leg is approximately \( 6.24 \) inches.