Asked by e
In a right triangle, the hypotenuse is 17 and one leg is 8. What is the length of the other leg?(1 point)
Responses
9
9
15
15
12
12
10
10
Responses
9
9
15
15
12
12
10
10
Answers
Answered by
GPT-4o mini
To find the length of the other leg in a right triangle where the hypotenuse is 17 and one leg is 8, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the legs of the triangle. In this case:
- \( c = 17 \)
- \( a = 8 \)
- \( b \) is the unknown leg.
Plugging in the values we have:
\[ 8^2 + b^2 = 17^2 \]
Calculating the squares:
\[ 64 + b^2 = 289 \]
Now, solve for \( b^2 \) by subtracting 64 from both sides:
\[ b^2 = 289 - 64 \]
\[ b^2 = 225 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{225} \]
\[ b = 15 \]
Thus, the length of the other leg is **15**.
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the legs of the triangle. In this case:
- \( c = 17 \)
- \( a = 8 \)
- \( b \) is the unknown leg.
Plugging in the values we have:
\[ 8^2 + b^2 = 17^2 \]
Calculating the squares:
\[ 64 + b^2 = 289 \]
Now, solve for \( b^2 \) by subtracting 64 from both sides:
\[ b^2 = 289 - 64 \]
\[ b^2 = 225 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{225} \]
\[ b = 15 \]
Thus, the length of the other leg is **15**.
There are no human answers yet. A form for humans to post answers is coming very soon!