Download Document

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
engineering
© The Visual Classroom
geography
physics
B
opposite
A
© The Visual Classroom
adjacent
C
B
adjacent
A
© The Visual Classroom
opposite
C
B
opposite
A
opp
sin A 
hyp
© The Visual Classroom
adjacent
adj
cos A 
hyp
C
opp
tan A 
adj
B
adjacent
A
opp
sin B 
hyp
© The Visual Classroom
opposite
adj
cos B 
hyp
C
opp
tan B 
adj
B
opp
A
adj
C
SOH CAH TOA
© The Visual Classroom
SOH
CAH
TOA
B
hy
p
10
A
8
C
6
adj
© The Visual Classroom
op
p
B
SOH
CAH
TOA
hy
p
5
adj
A
© The Visual Classroom
12
opp
C
Example 1: Determine side b
SOH
CAH
TOA
b
tan B 
8
b
tan 55 
8
b=
b=
© The Visual Classroom
B
55º
8 cm
A
ad
C j
b
opp
Example 2: Determine side c
if A is 31°.
B
hyp
13
cos 31 
c
A
13 cm
C
ad
j
SOH
CAH
TOA
© The Visual Classroom
Example 3: Determine side p if P is 45°.
R
Q
SOH
CAH
TOA
© The Visual Classroom
P
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.
hh
38º
20 m
The lighthouse is
© The Visual Classroom
m high.

© The Visual Classroom
B
SOH
CAH
TOA
opp
A
adj
C
opp
sin A 
hyp
adj
cos A 
hyp
opp
tan A 
adj
opp 
A  sin  
hyp 
 adj 
A  cos  
hyp 
opp 
A  tan  
 adj 
1
© The Visual Classroom
1
1
SOH
CAH
TOA
8
sin A 
10
1 8 
A  sin  
10 
A  53

© The Visual Classroom
6
cos A 
10
1 6 
A  cos  
10 
A  53

8
tan A 
6
18 
A  tan  
6 
A  53
Example 1: Determine the
measure of A.
8
tan A 
13
tan A = 0.6154
B
8 cm
opp
A
13 cm
A = tan-1(0.6154)
ad
j
A = 31.6°
© The Visual Classroom
C
SOH
CAH
TOA
Example 2: Determine the measure of P.
12
cos P 
17
R
SOH
CAH
TOA
cos P = 0.70588
P = cos–1(0.70588)
Q
P = 45.1
P
© The Visual Classroom
Example. 3: In DPQR, Q = 90°, PR = 8
cm and PQ = 4 cm. Find R.
hy
p
4
sin R 
8
sin R  0.5
R  sin
R  30

© The Visual Classroom
1
R
0.5
P
4 cm
Q
op
p
SOH
CAH
TOA
Example 4: Determine the
measure of B
B
3 cm
5
tan B 
3
tan B = 1.6666
B =
tan-1(1.6666)
B = 59.0°
© The Visual Classroom
A
5 cm
ad
C j
opp
SOH
CAH
TOA
Trigonometry Applications Problems
1. While walking to school you pass a barn with a silo. Looking up to the top of
the silo you estimate the angle of elevation to the top of the silo to be about
14°. You continue walking and find that you were around 40 m from the silo.
Using this information and your knowledge of trigonometric ratios calculate the
height of the silo.
© The Visual Classroom
2. A sailboat is approaching a cliff. The angle of elevation from the sailboat to the top of the
cliff is 35°. The height of the cliff is known to be about 2000 m. How far is the sailboat away
from the base of the cliff?
© The Visual Classroom
3. A sailboat that is 2 km due west of a lighthouse sends a signal to the
lighthouse that it is in distress. The lighthouse quickly signals a rescue plane
that is 7 km due south of the lighthouse. What heading from due north should
the plane take in order to intercept the troubled sailboat?
© The Visual Classroom
H/W:
Follow HW log
© The Visual Classroom