For the given right triangle, we want to write the ratio for the sine of $∠ A .$ Let's start by identifying the $hypotenuse$ of the triangle and the sides that are $opposite$ and $adjacent$ to $∠ A .$

We see that the length of the hypotenuse is

20 .

The length of the side adjacent to

∠ A

is

12

and the length of the side opposite to

∠ A

is

16 .

With this information, we can find the desired ratio. Recall how we calculate the sine ratio.

sin A = \frac{Length of leg opposite to ∠ A}{Length of hypotenuse}

Now, we can substitute our values to the above formula to find

sin A .

sin A = \frac{opposite}{hypotenuse}

SubstituteII

$opposite = 16$ , $hypotenuse = 20$

sin A = \frac{1 6}{2 0}

Finally, let's express the obtained fraction as a decimal. In order to do that, we can expand the fraction so that it has a denominator of

100 .

sin A = \frac{1 6}{2 0}

ExpandFrac

$\frac{a}{b} = \frac{a \cdot 5}{b \cdot 5}$

sin A = \frac{8 0}{1 0 0}

WriteDec

Write as a decimal

sin A = 0.80

Therefore, we have that the sine of

∠ A

is equal to

\frac{1 6}{2 0} = 0.80 .

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