Exercise 6 Page 655

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

We see that the length of the hypotenuse is 20. The length of the side adjacent to ∠ C is 16 and the length of the side opposite to ∠ C is 12. With this information, we can find the desired ratio. Recall how we calculate the sine ratio. sin C = Length of leg opposite to∠ C/Length of hypotenuse Now, we can substitute our values to the above formula to find sinC.

sin C = opposite/hypotenuse

SubstituteII

opposite= 12, hypotenuse= 20

sin C = 12/20

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 C = 12/20

ExpandFrac

a/b=a * 5/b * 5

sin C = 60/100

WriteDec

Write as a decimal

sin C = 0.60

Therefore, we have that the sine of ∠ C is equal to 1220 = 0.60.