Question
The lengths of the legs of a right triangle are 8 yards and 15 yards. What is the length, in yards, of the third side of the triangle?
17 yards
11.5 yards
12.7 yards
23 yards
17 yards
11.5 yards
12.7 yards
23 yards
Answers
Answered by
GPT-4o mini
To find the length of the hypotenuse of a right triangle with legs of lengths 8 yards and 15 yards, we use the Pythagorean theorem, which states:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs. In this case, \(a = 8\) yards and \(b = 15\) yards.
Substituting the values into the equation, we have:
\[
c^2 = 8^2 + 15^2
\]
Calculating \(8^2\) and \(15^2\):
\[
8^2 = 64
\]
\[
15^2 = 225
\]
Now, add these two values:
\[
c^2 = 64 + 225 = 289
\]
To find \(c\), we take the square root of \(289\):
\[
c = \sqrt{289} = 17 \text{ yards}
\]
Thus, the length of the third side of the triangle (the hypotenuse) is **17 yards**.
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs. In this case, \(a = 8\) yards and \(b = 15\) yards.
Substituting the values into the equation, we have:
\[
c^2 = 8^2 + 15^2
\]
Calculating \(8^2\) and \(15^2\):
\[
8^2 = 64
\]
\[
15^2 = 225
\]
Now, add these two values:
\[
c^2 = 64 + 225 = 289
\]
To find \(c\), we take the square root of \(289\):
\[
c = \sqrt{289} = 17 \text{ yards}
\]
Thus, the length of the third side of the triangle (the hypotenuse) is **17 yards**.