Exercise 22 Page 574

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 tangent of 60^(∘). Recall that the tangent of ∠ A is the ratio of the length of the leg opposite ∠ A to the length of the leg adjacent ∠ A. Using this definition, we can write the appropriate ratio for 60^(∘).

tan 60^(∘)=xsqrt(3)/x

ReduceFrac

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

tan 60^(∘)=sqrt(3)/1

DivByOne

a/1=a

tan 60^(∘)=sqrt(3)

UseCalc

Use a calculator

tan 60^(∘)=1.7320...

RoundDec

Round to 2 decimal place(s)

tan 60^(∘)≈1.73

The tangent of 60^(∘) is sqrt(3) or approximately 1.73.