Exercise 2 Page 665

We are given that a fan is seated in the upper deck of a stadium 200 feet away from home plate, and we're asked to evaluate the height at which the fan is sitting. Let's call this height h. We also know that the angle of depression to the field is 62^(∘). 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 62^(∘).

Since the figure is a right triangle, we can use one of the trigonometric ratios to evaluate the value of h. Let's recall that the sine of ∠ A is the ratio of the leg opposite ∠ A to the hypotenuse. Using this definition, we can create an equation for sin 62^(∘). sin 62^(∘)=h/200 Let's solve the above equation.

sin 62^(∘)=h/200

MultEqn

LHS * 200=RHS* 200

200sin 62^(∘)=h

RearrangeEqn

Rearrange equation

h=200sin 62^(∘)

UseCalc

Use a calculator

h=176.589...

RoundDec

Round to 1 decimal place(s)

h≈ 176.6

The fan is sitting at a height of approximately 176.6 feet.