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