Exercise 86 Page 462

Examining the diagram, we notice that this is a right triangle where one angle and its opposite side are known. If we label AB as x we can set up the following tangent ratio.

Let's solve this equation for x.

tan 54^(∘) =27/x

MultEqn

LHS * x=RHS* x

x tan 54^(∘) = 27

DivEqn

.LHS /tan 54^(∘).=.RHS /tan 54^(∘).

x = 27/tan 54^(∘)

UseCalc

Use a calculator

x = 19.61664...

RoundDec

Round to 2 decimal place(s)

x ≈ 19.62

The length of AB is about 19.62 units, which corresponds to option D.