Question

right triangle abc has side lengths
AB = 21
BC = 28
AC = 35
find the ratio of the side opposite C to the hypotenuse of triangle ABC. express your ratio as a decimal

Answer 1

In triangle ABC, with sides \( AB = 21 \), \( BC = 28 \), and \( AC = 35 \), we can identify the sides based on their lengths:

- The hypotenuse is the longest side, which is \( AC = 35 \).
- The side opposite to angle \( C \) is \( AB = 21 \).

To find the ratio of the side opposite angle \( C \) (which is \( AB \)) to the hypotenuse \( AC \), we can use the following formula:

\[
\text{Ratio} = \frac{\text{Opposite side}}{\text{Hypotenuse}} = \frac{AB}{AC} = \frac{21}{35}
\]

Now, we simplify the fraction:

\[
\frac{21}{35} = \frac{3}{5}
\]

Next, we convert this ratio into a decimal:

\[
\frac{3}{5} = 0.6
\]

Therefore, the ratio of the side opposite angle \( C \) to the hypotenuse of triangle ABC, expressed as a decimal, is

\[
\boxed{0.6}
\]