Final answer:
Using the Pythagorean theorem, the missing leg length of the triangle, given that one leg is 24 units and the hypotenuse is 26 units, is found to be 10 units.
Step-by-step explanation:
To find the length of the missing leg of a right triangle when you know the lengths of the other leg and the hypotenuse, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c^2 = a^2 + b^2 where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Given that one leg is 24 units long and the hypotenuse is 26 units long, you can set up the equation: 26^2 = 24^2 + b^2. Solving for b (the missing leg) would give us the answer.
First, square the lengths of the known leg and hypotenuse:
Then, substitute these values into the equation and solve for b^2:
676 = 576 + b^2
Subtract 576 from both sides:
b^2 = 676 - 576
b^2 = 100
Take the square root of both sides to find b:
b = \(\sqrt{100}\)
b = 10
So, the length of the missing leg is 10 units.