Exercise 5 Page 655

For the given right triangle, we want to write the ratios for the cosine 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 cosine ratio. cos C = Length of leg adjacent to∠ C/Length of hypotenuse Now, we can substitute our values to the above formula to find cosC.

cos C = adjacent/hypotenuse

SubstituteII

adjacent= 16, hypotenuse= 20

cos C = 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.

cos C = 16/20

ExpandFrac

a/b=a * 5/b * 5

cos C = 80/100

WriteDec

Write as a decimal

cos C = 0.80

Therefore, we have that the cosine of ∠ C is equal to 1620 = 0.80.