Exercise 16 Page 667

Let's begin with redrawing the given picture. We will name the consecutive letters.

Since we are asked to evaluate the length of AC, we need to find the value of x. To do this, we can use one of the trigonometric ratios. Let's recall that the tangent of ∠ A is the ratio of the leg opposite ∠ A to the leg adjacent ∠ A. Using this definition, we can create an equation for tan 70^(∘). tan 70^(∘)=30/x Let's solve the above equation.

tan 70^(∘)=30/x

MultEqn

LHS * x=RHS* x

xtan70^(∘)=30

DivEqn

.LHS /tan70^(∘).=.RHS /tan70^(∘).

x=30/tan 70^(∘)

UseCalc

Use a calculator

x=10.9191...

RoundDec

Round to 1 decimal place(s)

x≈ 10.9

The value of x is approximately 10.9 feet. Therefore, to find the distance between the worker standing on the ground and the truck, we will add this value and 10. AC= 10+10.9=20.9 The worker on the ground is standing approximately 20.9 feet from the truck.