Exercise 25 Page 656

Let's begin with drawing a 30^(∘)-60^(∘)-90^(∘) triangle. If we call the shorter leg of this right triangle x, then the longer leg is xsqrt(3) and the hypotenuse is 2x.

In our exercise we are asked to evaluate the sine of 30^(∘). Recall that the sine of ∠ A is the ratio of the length of the leg opposite ∠ A to the length of the hypotenuse. Using this definition, we can write the appropriate ratio for 30^(∘).

sin 30^(∘)=x/2x

ReduceFrac

a/b=.a /x./.b /x.

sin 30^(∘)=1/2

WriteDec

Write as a decimal

sin 30^(∘)=0.5

The sine of 30^(∘) is 12 or 0.5.