Question

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

The ratio of the side opposite <C to the hypotenuse is ____

Answer 1

To find the ratio of the side opposite angle C to the hypotenuse in triangle ABC, we first need to identify the lengths of the sides relative to angle C.

Given the side lengths:
- AB = 21 (this side is opposite angle C)
- BC = 28 (this side is adjacent to angle C)
- AC = 35 (this is the hypotenuse)

Thus, the side opposite angle C is side AB, which has a length of 21, and the hypotenuse AC has a length of 35.

Now, we calculate the ratio of the side opposite angle C to the hypotenuse:

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

To simplify this fraction:

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

Next, we convert this fraction to a decimal:

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

Therefore, the ratio of the side opposite angle C to the hypotenuse is:

\[
\boxed{0.6}
\]