Question

Right triangle ABC
has side lengths AB=21
, BC=28
, and AC=35
. Find the ratio of the side opposite ∠C
to the hypotenuse of triangle ABC
. Express your ratio as a decimal.(1 point)
The ratio of the side opposite ∠C
to the hypotenuse is

Answer 1

In triangle ABC, where \( AB = 21 \), \( BC = 28 \), and \( AC = 35 \), we can recognize that \( AC \) is the hypotenuse because it is the longest side. The side opposite angle \( C \) is segment \( AB \).

To find the ratio of the side opposite \( \angle C \) (which is \( AB \)) to the hypotenuse (which is \( AC \)), we can use the 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 can convert this ratio to a decimal:

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

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

\[
\boxed{0.6}
\]