Exercise 23 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 cosine of 30^(∘). Recall that the cosine of ∠ A is the ratio of the length of the leg adjacent ∠ A to the length of the hypotenuse. Using this definition, we can write the appropriate ratio for 30^(∘).

cos 30^(∘)=xsqrt(3)/2x

ReduceFrac

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

cos 30^(∘)=sqrt(3)/2

UseCalc

Use a calculator

cos 30^(∘)=0.86602

RoundDec

Round to 2 decimal place(s)

cos 30^(∘)≈ 0.87

The cosine of 30^(∘) is sqrt(3)2 or approximately 0.87.