Exercise 61 Page 690

We are given that Adelina is in a soccer stadium 80 feet above the field, and we are asked to evaluate the horizontal distance between Adelina and the soccer field. Let's call this distance d. We also know that the angle of depression to the field is 12^(∘). Let's sketch a diagram describing this situation.

As horizontal lines are parallel, the angle of depression and the angle of elevation are congruent, according to the Alternate Interior Angles Theorem. This means that the angle of elevation is also 12^(∘).

Since the figure is a right triangle, we can use one of the trigonometric ratios to evaluate the value of d. Let's recall that the tangent of ∠ A is the ratio of the leg opposite ∠ A to the leg adjacent this angle. Using this definition, we can create an equation for tan 12^(∘). tan 12^(∘)=80/d Let's solve the above equation.

tan 12^(∘)=80/d

MultEqn

LHS * d=RHS* d

dtan 12^(∘)=80

DivEqn

.LHS /tan 12^(∘).=.RHS /tan 12^(∘).

d=80/tan 12^(∘)

UseCalc

Use a calculator

d=376.3704...

RoundDec

Round to 1 decimal place(s)

d≈ 376.4

The horizontal distance between Adelina and the soccer field is approximately 376.4 feet.