To find the length of the missing leg (b) in a right triangle with legs of lengths 10 yards and 8 yards, we can use the Pythagorean theorem.
The Pythagorean theorem states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
In this case, let’s assume 10 yards is the hypotenuse (if it is in line with being the longest side), otherwise, we can also write the equation using a as one leg and b as another leg.
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If we assume 10 yards is the hypotenuse: \[ 8^2 + b^2 = 10^2 \] \[ 64 + b^2 = 100 \] \[ b^2 = 100 - 64 \] \[ b^2 = 36 \] \[ b = \sqrt{36} = 6 , \text{yards} \]
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If, however, we were treating the 10 yards as one leg, we can also switch roles: \[ 10^2 + b^2 = 8^2 \] However, this doesn’t compute because the sum of the squares of the legs must equal the square of the hypotenuse being the largest side.
So the correct interpretation with \( 10 , yd \) as the hypotenuse leads to:
The length of the missing leg \( b \) is: \[ b = 6 , \text{yards} \]
Thus, \( b = 6 \) yards.