Question

26ft, a, 10ft
What is the length of the missing leg? If necessary, round to the nearest tenth.
a=
feet

Answer 1

To find the length of the missing leg in a right triangle, we can use the Pythagorean theorem, which states:

\[ a^2 + b^2 = c^2 \]

where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the other two legs.

In your case, the hypotenuse \( c \) is 26 ft and one leg \( b \) is 10 ft. We need to solve for the missing leg \( a \).

Using the Pythagorean theorem:

\[ a^2 + 10^2 = 26^2 \]

Calculating the squares:

\[ a^2 + 100 = 676 \]

Now, subtract 100 from both sides:

\[ a^2 = 676 - 100 \]
\[ a^2 = 576 \]

Next, take the square root of both sides to find \( a \):

\[ a = \sqrt{576} \]
\[ a = 24 \]

Therefore, the length of the missing leg \( a \) is **24 feet**.