Exercise 1 Page 655

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 = Length of leg opposite to∠ A/Length of hypotenuse Now, we can substitute our values to the above formula to find sinA.

sin A = opposite/hypotenuse

SubstituteII

opposite= 16, hypotenuse= 20

sin A = 16/20

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 A = 16/20

ExpandFrac

a/b=a * 5/b * 5

sin A = 80/100

WriteDec

Write as a decimal

sin A = 0.80

Therefore, we have that the sine of ∠ A is equal to 1620 = 0.80.