Exercise 50 Page 757

Let's take a look at the given diagram. Let x represent the height of the theodolite.

Since we are given that the angle of elevation is 62.7^(∘), we can use one of the trigonometric ratios to evaluate the value of x. 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 62.7^(∘). tan 62.7^(∘)=x/83 Let's solve the above equation.

tan 62.7^(∘)=x/83

MultEqn

LHS * 83=RHS* 83

83tan62.7^(∘)=x

RearrangeEqn

Rearrange equation

x=83tan62.7^(∘)

UseCalc

Use a calculator

x=160.8095...

RoundDec

Round to 1 decimal place(s)

x≈ 160.8

The theodolite has a height of approximately 160.8 meters. To find the height of the ceiling we need to add 1.5 to the height of the theodolite. 160.8+ 1.5=162.3 The height of the ceiling is approximately 162.3 meters. Notice that this is only an approximation, as we used approximate values to evaluate it.