The word trigonometry means

1
Trigonometry
The word trigonometry means triangle
measurement. You can use trigonometry to
calculate the lengths of sides and the measures
of angles in triangles.
Trigonometry has been used for centuries in the
study of
surveying
astronomy
geography
physics
engineering
2
Parts of a Right Triangle
B
hypotenuse
opposite
A
C
adjacent
3
B
hypotenuse
adjacent
C
opposite
A
4
B
hypotenuse
opposite
A
C
adjacent
5
B
hypotenuse
adjacent
C
opposite
A
6
B
hyp
opp
C
A
adj
TOA
SOH
CAH
7
B
SOH CAH TOA
hyp
10
opp
8
A
C
6
adj
8
SOH CAH TOA
B
hyp
13
5
adj
A
12
C
opp
9
Example 1 Determine side b
B
SOH CAH TOA
55º
8 cm
adj
b
A
C
opp
b 8 tan 55
b 11.4 cm
10
Example 2 Determine side c if ?A is 31.
B
hyp
A
C
13 cm
adj
c 15.2
SOH CAH TOA
11
Example 3 Determine side p if ?P is 45.
opposite
R
Q
p 12.0
17 cm
SOH CAH TOA
P
hypotenuse
12
Ex. 4 From a distance of 20 m from the base a
lighthouse the angle of elevation to the top of a
lighthouse is 38º. Determine the height of the
lighthouse.
h
h
h 20 tan 38
38º
h 20 (0.7813)
20 m
h 15.6
The lighthouse is 15.6 m high.