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TrigonometryTrigonometry
A S 12.3.5
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h
o
ehypoteneus
oppositeAsin =
ha
hypotenuseadjacentAcos =
a
o
adjacent
oppositeAtan =
In a 900
triangle:h2 = o2 + a2
Pythagoras
The ratios of the sidesare defined as:
adjacent
hy
potenuse
oppos
it
e
A
Triangle ActionTriangle Action
sin B = 3/5
e.g. 5
4
3
B
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Lets ReviseLets Revise
Calculate the unknown side:
For 500 angle;givenadjacent;need opposite
For 400 angle;given opposite;
needhypotenusetan 50 = y/9
y = 9 . tan 50
10,73
sin 40 = 8/x
x = 8/sin 40
12,45
5009
y
400
x8
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Calculate the unknown angle:
For angle A;given adjacent;given
hypotenusecos A = 8/17
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Morgan Point is 6
km east and 4 kmnorth of CapePoint. Cape Point
Morgan
Point
4km
6km
N
Steve sails directly fromCape Point to MorganPoint. What is his
bearing?
A
tan A = 6/4
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IfIf not 90not 9000
Use sine rule:
c
C
b
B
a
A sinsinsin= B C
A
a
bc
Find the length of EF.
EF
60sin
13
55sin=
60sinEF 13.55sin. =
EF= cm7413,
550
600
13cm
D
E F
e.g.
1
Always makesure your angleis opposite theside to form a
ratio.
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A
B C460
19cm
31cm
Determine
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Use cosine rule:
Calculate BC if in ABC,
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ab
cbaCosC
2
222 =
01,34C
8cm
12
cm
7cmA
B
C
c
ab
8122
7812222
=CosC
Calculate
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Area rule: (If height is not given.)3
B C
A
a
bcArea ABC = a b sin CorArea ABC = a c sin B orArea ABC = b c sin A
The angle used always lies between two sides.i.e.
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A space shuttle is tied
down by two 120 m longchains. The angle ofelevation is 65,380.Calculate the distance
between the tie downpoints on the ground.
ApplicationsApplications
distance
65,38
120120
S
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P shows a point where
a penalty kick is takenfrom in a rugby match.The distance betweenthe posts is 5,5m.
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A and B are two points on oppositessides of tower CD. AB = 170m and
angles of elevation from A and B are41,50 and 58,10 respectively.Find the size of
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630kmN(Nelspruit
P(Polokwane)
230
M(Bloemfontein)
675
km
The navigationtriangle shows the
distances to fly fromBloemfontein to Pand N.Determine the distance
from Nelspruit toPolokwane.
NP2 = 6752 + 6302 2x675x630xcos230
= 69635NP = 263,89 km
Calculate the area enclosed by thenavigation triangle.Area = x 675 x 630 x sin230
= 83 079,21 km2
4.N
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Mr Ndaki bought farm land that has atriangular shape. The area A of the farm =
1024 m2
. The length of side PR= 59 m and