January 18th in your BOOK, 4.2

copyright2009merrydavidson

Happy Birthday to: Hira Saleem, Shayna Faith Richardson, Georgi Longee, Davin Henderson & Morgan Hatwig

Get a calculator. Put the “mode” in degrees.

Special Right Triangles

S O H C A H T O A

opp

adj

opp

hyp

adj

hyp

hyp

opp

hyp

adj

adj

opp

S O H C A H T O A

y

x

rReciprocal functionsParent functions

Angles of elevation and depression (calculator)

Line of Sight

Angle of depression (you look DOWN)

Line of Sight

Angle of elevation (you look up)

Definitions

• An ANGLE OF ELEVATION is the angle between a horizontal line of sight from an observer to an object at a higher level.

• An ANGLE OF DEPRESSION is the angle between a horizontal line and the line of sight from an observer to an object at a lower level. (This is OUTSIDE of the special right triangle.)

1) The angle of depression is measured from the top of a 43 ft tower to a reference point on the ground. Its value is found to be 63o. How far is the base of the tower from the point on the ground?

This line MUST be drawn in.

21.9 ft.

This line MUST be drawn in.

30.7 ft.

2) The angle of depression from a search light to its target is 58o. How long is the beam of light, if the searchlight is 26 ft above ground?

89.4 ft.

3) A NASA recovery helicopter hovers 75 ft above a space capsule. If the angle of depression to the recovery ship is 40o, how far is the ship from the space capsule?

4) Given 2 sides, find the included angle.

A historic lighthouse is 200 yards from a bike path along the edge of a lake. A walkway to the lighthouse is 400 yards long. Find the acute angle between the bike path and the walkway.

200 yds

walkway400 yds

What do you know? 200 1sin

400 2

opp

hyp

So what is the angle measure? 30o

Bik

e p

ath

5) Given 2 sides, find the included angle.A historic lighthouse is 200 yards from a bike path

along the edge of a lake. A walkway to the lighthouse is 350 yards long. Find the acute angle between the bike path and the walkway.

200 yds

350 yds

200sin

350

opp

hyp So what is the angle

measure?Take sin-1 of each side.

1 1 200sin sin sin350

35

Bik

e p

ath

10 degrees

6) Find the angle of elevation from the bottom of the world’s longest slide, located in Peru, Vermont if the vertical drop of the ladder is 82 feet and the length of the slide is 460 feet.

46082

?

82sin

460

1 82sin460

HW: WS 6-4