Transcript 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