2

Make sure the calculator is in Degree Mode (DRG button)

Practice getting the sine/cos/tan of various angles

Inverse functions: [2nd F button] Use of backets is important when finding inverses:e.g

Some considerations

53SinA

53in If

1-

AS

SECTION 1

RIGHT ANGLED TRIANGLES

RIGHT ANGLED TRIANGLES

HYPOTHENUSE

900 A

OPPO

SITE

ADJACENT

HYPOTHENUSE

900

A

OPPOSITE

ADJACENT

a

b

c

a2 +b2 = c2

PYTHAGORAS THEOREM

The square of the hypotenuse is equal to the sum of the squares on the other 2 sides.

This theorem is used when you are looking for the length of one side of a triangle when you are given the measurements of the other 2 sides.( Remember this theorem only works for right angled triangles).

Hypotenuse [H]

Hypotenuse [H]

A

Opposite [O]

Adjacent [A]

Hypotenuse [H]A

Opposite [O]

Adjacent [A]

[H]

A

[O]

[A]

Cosine

Cos A = A

H

Sine

Sin A = O

H

Tangent

Tan A = O

A

SOHCAHTOA

[5][3]

[4]

A

SOHCAHTOA

[H][O]

[A]

Sin A =OH

=35

[5]

A

[3]

[4]

SOHCAHTOA

[H][O]

[A]

Cos A =AH

=45

[3]

SOHCAHTOA

[H] [5]

A

[4]

[O]

[A]

Tan A =OA

=34

[13]

A

[12]

[5]

SOHCAHTOA

[H][O]

[A]

Sin A =OH

=1213

[13]

A

[12]

[5]

SOHCAHTOA

[H][O]

[A]

Cos A =AH

=513

[13]

A

[12]

[5]

SOHCAHTOA

[H][O]

[A]

Tan A =OA

=125

[15]

300

x

SOHCAHTOA

[H][O]

[A]

Sin 300 =OH

= x15

Looking for x OGiven H

Sin 300 = 0.5

x15

0.51

=

x = 15(0.5)

= 7.5

[15]

500

x

SOHCAHTOA

[H][O]

[A]

tan 50o =OA

= x15

Looking for x OGiven A

Tan 50o = 1.1917

x = 15(1.1918)

= 17.876

x15

1.19171

=

[15]

35o 16’

x

SOHCAHTOA

[H][O]

[A]

Cos 35o 16’ =AH

= 15x

Looking for x HGiven A

Cos 35o 16’ = 0.8164

x(0.8165) = 15

x =

15x

0.81641

=

150.8165

= 18.37

THE ANGLE OF ELEVATION AND DEPRESSION

(b) Angle of elevation = Angle looking up

depression

elevation

(a) Angle of depression = Angle looking down

Example 1A plane takes of at an angle of 200 to the level ground. After flying for 100m how high is it off the ground.

200

100m

height

900

QUESTIONS ON RIGHT ANGLED TRIANGLES

200

100mheight

900

HYP opp

In this we are given the Hyp. And we are looking for the Opp

So we use the Sin Formula

100h

HypOpp 20Sin Sin20 0.3420

100

h.3420 h 34.2m

2. A building 14m heigh casts a shadow 10m in length Find the angle of elevation of the sun.Example

x

10m

14m

AdjOppx Tan 4.1

1014x Tan

x 54 28'

3. A ladder 10m long just reaches the top of a wall 8m high. Find the angle between the ladder and the wall.Example

10m8m

HypAdj Cos

8.108 Cos

53' 36

25 4. If Cos , find Sin and Tan , 0 9013

without using calculator.

Example

Note: If given ratio always draw right angled triangle

135

HypAdj Cos

222 5x13 Pythagoras By

triplet)(Note 12x

Adj = 5

Hyp = 13x

1312

HypOpp Sin

22 ) (Tan Tan 25144

512

AdjOpp 22