#### Right-angled Trigonometry

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Right-angled Trigonometry

Right-angled Trigonometry
A
Right-angled Trigonometry
Opposite
A
Right-angled Trigonometry
Hypotenuse
A
Opposite
Right-angled Trigonometry
Hypotenuse
A
Adjacent
Opposite
Right-angled Trigonometry
Opp
Sin A
Hyp
Hyp
A
Adj
Opp
Right-angled Trigonometry
Hyp
A
Adj
Opp
Opp
Sin A
Hyp
Adj
Cos A
Hyp
Right-angled Trigonometry
Hyp
A
Adj
Opp
Opp
Sin A
Hyp
Adj
Cos A
Hyp
Opp
T an A
Adj
Right-angled Trigonometry
Hyp
A
Opp
Opp
Sin A
Hyp
Adj
Cos A
Hyp
Opp
T an A
Adj
Adj
The Old Arab
Right-angled Trigonometry
Hyp
A
Adj
Opp
Opp
Sin A
Hyp
Adj
Cos A
Hyp
Opp
T an A
Adj
The Old Arab Sat On His
Right-angled Trigonometry
Hyp
A
Adj
Opp
Opp
Sin A
Hyp
Adj
Cos A
Hyp
Opp
T an A
Adj
The Old Arab Sat On His Camel And Hiccupped
Example
Calculate the length of PQ in the triangle
PQR
P
R
52 cm
32
Q
Example
Calculate the length XY in the triangle XYZ
X
59
4.6 cm
Z
Y
Example
Calculate the length of BC in the triangle
ABC.
B
5 cm
A
24
C
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
B
4 cm
A
6 cm
C
Example
Find the size of angle x in each of the
following
(i)
1.2 cm
x
4.7 cm
(ii)
x
10 cm
3.7 cm
(iii)
7 cm
x
12 cm
Example
Calculate the size of angle PQR in the
triangle below.
P
8 cm
P
8 cm
6 cm
R
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
E
a) the length of AC
b) the angle EAH
A
D
H
B
C
Example
ABCDEF is a prism with a triangular crosssection. , BC = 8m, AB = 6m and CD =
20m.
E
Find
(i) AC
(ii) BD
F
D
A
(iii) the total
surface area
of the prism.
B
C