Exercise 37 Page 669

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 25. The length of the side adjacent to ∠ A is 15 and the length of the side opposite to ∠ A is 20. With this information, we can find the desired ratio.

sin A=opposite/hypotenuse

SubstituteII

opposite= 20, hypotenuse= 25

sin A=20/25

ReduceFrac

a/b=.a /5./.b /5.

sin A=4/5

CalcQuot

Calculate quotient

sin A=0.80

The value of sin A is 45 or 0.80.