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Right-angled Trigonometry. A. Right-angled Trigonometry. Opposite. A. Right-angled Trigonometry. Hypotenuse. Opposite. A. Right-angled Trigonometry. Hypotenuse. Opposite. A. Adjacent. Right-angled Trigonometry. Opp. Hyp. A. Adj. Right-angled Trigonometry. Opp. Hyp. A. Adj. - PowerPoint PPT Presentation
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Right-angled Trigonometry
A
Right-angled Trigonometry
A
Opposite
Right-angled Trigonometry
A
OppositeHypotenuse
Right-angled Trigonometry
A
OppositeHypotenuse
Adjacent
Right-angled Trigonometry
A
OppHyp
Adj
Hyp
OppSin A
Right-angled Trigonometry
A
OppHyp
Adj
Hyp
OppSin A
Hyp
AdjCos A
Right-angled Trigonometry
A
OppHyp
Adj
Hyp
OppSin A
Hyp
AdjCos A
Adj
OppTan A
Right-angled Trigonometry
The Old Arab
A
OppHyp
Adj
Hyp
OppSin A
Hyp
AdjCos A
Adj
OppTan A
Right-angled Trigonometry
The Old Arab Sat On His
A
OppHyp
Adj
Hyp
OppSin A
Hyp
AdjCos A
Adj
OppTan A
Right-angled Trigonometry
The Old Arab Sat On His Camel And Hiccupped
A
OppHyp
Adj
Hyp
OppSin A
Hyp
AdjCos A
Adj
OppTan A
Example
Calculate the length of PQ in the triangle PQR
32
52 cm
Q
R P
Example
Calculate the length XY in the triangle XYZ
59
4.6 cm
Z
X
Y
Example
Calculate the length of BC in the triangle ABC.
24
5 cm
A
C
B
Example
A surveyor, P, is 1000m away on
horizontal ground from the foot of a radio
mast, QR. From P the angle of elevation of
the top, R, of the mast is 20. Find the
height of the mast. Assume the surveyor’s
height to be negligible.
Example
From the top of a vertical cliff 100m high
the angle of depression of a boat out at
sea is 32. How far is the boat from the
foot of the cliff?
Example
Calculate the size of angle A in the triangle ABC
6 cm
4 cm
A C
B
Example
Find the size of angle x in each of the following
(i)
4.7 cm
1.2 cm
x
(ii)
10 cm3.7 cm
x
(iii)7 cm
12 cm
x
Example
Calculate the size of angle PQR in the triangle below.
8 cm 8 cm
6 cm
P
RP
Example
The road from village A runs due West for
5 miles to a fort B. A television mast is due
South of B and 4 miles from B. Find the
distance and bearing of the mast from A.
Example
The figure is a pyramid on a square base ABCD. The edges of the base are 30cm long and the height, EH, of the pyramid is 42cm. Find
a) the length of AC
b) the angle EAH
E
C
D
B
A
H
Example
ABCDEF is a prism with a triangular cross-section. , BC = 8m, AB = 6m and CD = 20m.
Find
(i) AC(ii) BD
(iii) the total surface
area of the prism.
A F
E
CB
D
