Question

If a right triangle has a leg with length 12 in and the hypotenuse is 16 in., the other leg must be approximately blank in
11.5, 10.6, 20, 8.6

Answer 1

To find the length of the other leg of a right triangle when one leg and the hypotenuse are known, we can use the Pythagorean theorem, which states:

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

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

In this case, let’s let \( a = 12 \) in (one leg) and \( c = 16 \) in (the hypotenuse). We want to find \( b \) (the other leg).

Plugging the known values into the equation:

\[ 12^2 + b^2 = 16^2 \]

Calculating the squares:

\[ 144 + b^2 = 256 \]

Now, subtract 144 from both sides:

\[ b^2 = 256 - 144 \]
\[ b^2 = 112 \]

Now, take the square root of both sides to find \( b \):

\[ b = \sqrt{112} \]

Calculating the square root:

\[ b \approx 10.583 \]

Rounding to one decimal place gives \( b \approx 10.6 \).

So the approximate length of the other leg is \( \boxed{10.6} \) inches.