TOPIC: TRIGONOMETRY Aim: To be able to name the sides of a right angled triangle (RAT) given and interior angle.

1
TOPIC TRIGONOMETRYAim To be able to name the
sides of a right angled triangle (RAT) given and
interior angle.

• Identify the names of the sides of these right
  angled-triangles given angle k
• What can you say about the names of the sides?
• They are named according to the angle under
  consideration.

opposite
b
opposite
a
b
c
c
adjacent
hypotenuse
hypotenuse
a
k
opposite
a
adjacent
k
c
adjacent
hypotenuse
b
k
opposite
c
hypotenuse
b
k
a
adjacent
2
TOPIC TRIGOOMETRYAim To Understand the 3
Trigonometric Ratios

• The 3 ratios are Sine, Cosine and Tangent
• Using pneumonic, the ratios are SOH, CAH, TOA

3
TOPIC TRIGONOMETRYAim To use Trigonometry to
find lengths,given an interior angle and one
side of a RAT

• Finding the length of an unknown side of a right
  angled triangle
• The appropriate ratio to use is Tangent, i.e. TOA
• Tan 260 a/7
• a/7 Tan 260
• a 7 x Tan 260
• a 7 x 0.4877
• a 3.41cm (to 2 d.p.)

• Calculate the length of y.
• NB The appropriate ratio is sine, SOH
• Sine 340 y/5
• y/5 Sine 340
• y 5 x Sine 340
• y 5 x 0.559
• y 2.80m (to 2 d.p.)

(hypotenuse)
5m
y
a
(opposite)
(opposite)
34o
26o
(adjacent)
7cm
4
TOPIC TRIGONOMETRYQuestions for Students to
Attempt.

• Calculate the length of y
• NB The appropriate ratio is Sine, i.e. SOH
• Sine 420 y/6.2
• y/6.2 Sine 420
• y 6.2 X Sine 420
• y 6.2 X 0.669
• y 4.19m (to 2 d.p.)

• Calculate the length of side x
• The appropriate ratio to use is Cosine, i.e. CAH
• Cos 670 x/10.6
• 0.39 x/10.6
• x 10.6 X 0.39
• x 4.14m (to 2 d.p.)

y
(Opposite)
Hypotenuse
10.6m
Hypotenuse
670
6.2m
420
x
(Adjacent)
5
TOPIC TRIGONOMETRYStarter

• Evaluate the following
• Tan 50
• Sin 50
• Cos-1 0.56
• Tan-1 40
• Sin-10.50

1.19
0.76
55.94
88.85
30
6
TOPIC TRIGONOMETRYAim To Find an interior
angle of a RAT

• NB The appropriate ratio is
• Sine , i.e. SOH
• Sine y 30/50
• Sine y 0.6
• y Sine-1 0.6
• y 36.90, approximately 370

• To find angle a
• The appropriate ratio to use is Tangent, i.e. TOA
• Tan a 32/25
• Tan a 1.28
• a Tan -1 1.28
• a 52.00

• To find the size of angle y

32cm
(Opposite)
50cm
25cm
(Opposite)
Hypotenuse
30cm
a
Adjacent
y0
7
TOPIC TRIGONOMETRYQuestions for students to
attempt.

• Find angle y
• NB The appropriate ratio is Cosine, i.e. CAH
• Cos y 12.4/19.7
• Cos y 0.639
• y Cos-1 0.639
• y 50.280
• y is approximately 500

• Find angle b
• The appropriate ratio to use is Sine, i.e. SOH
• Sin b 6/12
• Sin b 0.5
• b Sin-1 0.5
• b 300

(Adjacent)
12.4m
Hypotenuse
Opposite
y
12cm
6cm
Hypotenuse
b
19.7m
8
TOPIC TRIGONOMETRYAim To Use Trigonometry to
Solve Problems

• Key words
• Angle of Elevation is an angle between the
  horizontal and an object above it
• Angle of Depression /Descent is an angle
  between the horizontal and an object below it
• Tips Draw and label your diagram
• Write down the formula to be used and calculate
  the answer

9
TOPIC TRIGONOMETRYAim To Use Trigonometry to
Solve Problems

• The angle of descent is outside the right
  angled-triangle. So we need to find the angle
  inside it.
• TOA is the ratio to use
• 4500/a Tan 400
• 4500/a 0.8390
• a 4500 / 0.8390
• a 5363.52m

• An aeroplane is 4500m from touchdown.
• Its angle of descent is 500 to horizontal. How
  high is it above the ground.

500
400
a
Runway Ground
4500m
Touchdown
10
TOPIC TRIGONOMETRYAim To Use Trigonometry to
Solve Problems

• A boat is due South of a Lighthouse.
• It sails on a bearing 0450 until it is due east
  of the lighthouse. If the boat is now 50km away
  from the lighthouse, how far has it sailed.

• The appropriate ratio is SOH
• Sin 450 50/a
• 0.71 50/a
• a 50 / 0.71
• a 70.42km

50km
(Opposite)
East
a
Hypotenuse
0450
South