Algebra 1 Common Core Student Edition, Grade 8-9

t ) G o t It? 4. In a right triangle, th e side opposite LA is 8 m m long an d th e h ypotenuse is

12 m m long. W hat is th e m easure of LAI

You can use trigonom etric ratios to m easure som e distances indirectly. To m easure such

distances, it is often convenient to use an angle o f elevation or an angle o f depression.

An angle of elevation is an angle from the

horizontal up to a line of sight.

• 
  
  
  
  • 
    
    
    
    • J Angle of depression
      Une««ghi.........................
      Angle of e le v a tio n ']'
    
    
    
    
  
  
  
  

An angle of depression is an angle from the

horizontal dow n to a line of sight.

W hen you solve real-w orld p roblem s using

trigonom etric ratios, you often n e e d to

ro u n d your answers. The problem m ay tell

you how to round. Otherwise, ro u n d your

answ ers to th e precision of th e m easu rem en ts u sed in th e problem. For instance, if the

problem has m easu rem en ts to the n ea rest 10 ft, ro u n d your answ er to the n ea rest 10 ft.

EH353DUsing an Angle of Elevation or Depression

Ri d es Suppose you are waiting in line for a ride. You see your friend at

the top of the ride. How far are you from the base of the ride?

Ibjnk,

150 f t

Whi c h r a t i o s h o u l d

you use?

You know the length

of the opposite leg and

want to find the length

of the adjacent leg. Use

the tangent ratio.

ta n 20° =

opposite leg

adjacent leg

ta n 20° = —

x ( ta n 20°) = 150

x = 150

x ~

x = 410

tan 20°

412.1216129

Use th e ta n g e n t ratio.

Substitute 150 and x from the diagram.

M u ltip ly each side by x.

Divide each side by tan 20°.

Use a calculator.

Round to the nearest 10 ft.

You are ab o u t 410 ft from th e base of th e ride.

G o t It? 5. After you m ove forw ard in th e line, th e angle of elevation to th e top of the

ride becom es 50°. How far are you from th e base of th e ride now?

648 Chapter 10 Radical Expressions and Eq uat io ns