Asked by Alto Saxaphone
A right triangle has a hypotenuse that is 17 centimeters long and one side that is 15 centimeters long. What is the length of the other side of the triangle?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the length of the other side of the right triangle, 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 lengths of the other two sides. In this case, we know the hypotenuse \( c = 17 \) cm and one side \( a = 15 \) cm. We need to find the length of the other side \( b \).
Plugging the known values into the Pythagorean theorem:
\[
15^2 + b^2 = 17^2
\]
Calculating \( 15^2 \) and \( 17^2 \):
\[
225 + b^2 = 289
\]
Next, we can subtract 225 from both sides to solve for \( b^2 \):
\[
b^2 = 289 - 225
\]
\[
b^2 = 64
\]
Now, taking the square root of both sides to find \( b \):
\[
b = \sqrt{64}
\]
\[
b = 8
\]
Therefore, the length of the other side of the triangle is \( \boxed{8} \) centimeters.
\[
a^2 + b^2 = c^2
\]
where \( c \) is the hypotenuse and \( a \) and \( b \) are the lengths of the other two sides. In this case, we know the hypotenuse \( c = 17 \) cm and one side \( a = 15 \) cm. We need to find the length of the other side \( b \).
Plugging the known values into the Pythagorean theorem:
\[
15^2 + b^2 = 17^2
\]
Calculating \( 15^2 \) and \( 17^2 \):
\[
225 + b^2 = 289
\]
Next, we can subtract 225 from both sides to solve for \( b^2 \):
\[
b^2 = 289 - 225
\]
\[
b^2 = 64
\]
Now, taking the square root of both sides to find \( b \):
\[
b = \sqrt{64}
\]
\[
b = 8
\]
Therefore, the length of the other side of the triangle is \( \boxed{8} \) centimeters.
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