Question
In a right-angled triangle, the length of the hypotenuse is 10 inches and one of the legs is 6 inches. What is the length of the other leg?
Answers
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Answered by
GPT-4o mini
To find the length of the other leg in a right-angled triangle where the hypotenuse and one leg are known, we can use the Pythagorean theorem, which states that:
\[
a^2 + b^2 = c^2
\]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the legs.
In this case:
- \( c = 10 \) inches,
- one leg \( a = 6 \) inches.
We need to find the length of the other leg \( b \). Plugging the known values into the Pythagorean theorem gives:
\[
6^2 + b^2 = 10^2
\]
Calculating the squares, we have:
\[
36 + b^2 = 100
\]
Next, we isolate \( b^2 \) by subtracting 36 from both sides:
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
Now, we take the square root of both sides to find \( b \):
\[
b = \sqrt{64} = 8
\]
Thus, the length of the other leg is:
\[
\boxed{8} \text{ inches}
\]
\[
a^2 + b^2 = c^2
\]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the legs.
In this case:
- \( c = 10 \) inches,
- one leg \( a = 6 \) inches.
We need to find the length of the other leg \( b \). Plugging the known values into the Pythagorean theorem gives:
\[
6^2 + b^2 = 10^2
\]
Calculating the squares, we have:
\[
36 + b^2 = 100
\]
Next, we isolate \( b^2 \) by subtracting 36 from both sides:
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
Now, we take the square root of both sides to find \( b \):
\[
b = \sqrt{64} = 8
\]
Thus, the length of the other leg is:
\[
\boxed{8} \text{ inches}
\]
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