Final answer:
To find the missing leg 'b' in a right triangle where 'a' is 25 yards and 'c' equals 'b', we use the Pythagorean theorem. We find 'b' by calculating b = √(25² - 20²), which results in 'b' being 15 yards.
Step-by-step explanation:
To find the missing leg length in a right triangle using the Pythagorean theorem, we start with the formula a² + b² = c², where 'a' and 'b' are the lengths of the legs of the triangle, and 'c' is the length of the hypotenuse. Here we are given that 'a' is 25 yards and 'c', which usually represents the hypotenuse, equals 'b', which is the unknown leg we need to find.
We can rearrange the formula to solve for 'b' by subtracting 'a²' from both sides, giving us b² = c² - a². Since c = b in this case, this becomes b² = b² - a². To solve for 'b', we simply take the square root of both sides after plugging in the known values.
So the equation to find 'b' would be b = √(25² - 20²) = √(625 - 400) = √225. After calculating, we find that 'b' is 15 yards. Hence, the length of the missing leg 'b' is 15 yards.