Question

Right triangle ABC has side lengths AB = 21, BC = 28, and AC = 35. Find the ration of the side opposite angle C to the hypotenuse of triangle ABC. Express your ration as a decimal.

The ration of the side opposite angle C to the hypotenuse is ___.

Answer 1

In triangle ABC, where \(AB = 21\), \(BC = 28\), and \(AC = 35\), we first need to confirm that \(AC\) is indeed the hypotenuse. In a right triangle, the hypotenuse is the longest side, and here \(AC\) is the longest because \(35 > 28 > 21\).

Now, we need to find the ratio of the side opposite angle \(C\) to the hypotenuse \(AC\). The side opposite angle \(C\) is \(AB\), which is given as \(21\), and the hypotenuse \(AC\) is \(35\).

We will calculate the ratio:

\[
\text{Ratio} = \frac{\text{Side opposite angle C}}{\text{Hypotenuse}} = \frac{AB}{AC} = \frac{21}{35}
\]

Next, we can simplify this fraction. Both \(21\) and \(35\) can be divided by their greatest common divisor, which is \(7\):

\[
\frac{21}{35} = \frac{21 \div 7}{35 \div 7} = \frac{3}{5}
\]

Now, we need to express this ratio as a decimal:

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

Thus, the ratio of the side opposite angle \(C\) to the hypotenuse of triangle \(ABC\) is

\[
\boxed{0.6}
\]