www. trigonometry: the study of triangles (sides and angles) physics surveying trigonometry has...
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A B C adjacent opposite h y p o t e n u s eTRANSCRIPT
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Trigonometry: The study of triangles (sides and angles)
physics
surveying
Trigonometry has been used for centuries in the study of:
astronomygeography
engineering
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A
B
Cadjacent
hypotenuse
opposite
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A
B
C
adjacent
opposite
hypotenuse
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A
B
C
opposite
adjacent
hypotenuse
oppsinhyp
A adjcoshyp
A opptanadj
A
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A
B
Copposite
adjacenthypotenuse
oppsinhyp
B adjcoshyp
B opptanadj
B
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A
B
C
opp
adj
hyp
SOH CAH TOA
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A
B
C
8
6
10
sin A cos A tan A
opp
adj
hyp
SOHCAHTOA
810
610
86
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A
B
C
3
4
5
sin B cos B tan B
adj
opp
hypSOHCAHTOA
45
35
43
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A
B
C
5
12
13
sin B cos B tan B
adj
opp
hyp
SOHCAHTOA
1213
513
125
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sin 21° =
cos 53° =
tan 72° =
0.3584
0.6018
3.0777
Use a calculator to determine the following ratios.
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sin A = 0.4142
cos B = 0.6820
tan C = 1.562
A = sin-1(0.4142)
B = cos-1(0.6820)
C = tan-1(1.562)
= 24°
= 47°
= 57°
Determine the following angles (nearest degree).
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Determine the following angles (nearest degree).
sin A =
cos B =
tan C =
A = sin-1(0.5833)
B = cos-1(0.2666)
C = tan-1(1.875)
= 36°
= 75°
= 62°
712
415
158
= 0.5833
= 0.2666
= 1.875
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A
B
C
a6 cm
Example 1: Determine side a
30º
a = 6 sin 30°
a = 3 cm
a = 6 (0.5)sin
6A a
sin 306a
hypopp
SOHCAHTOA
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A
B
C
50º
b
9 m
40º
Ex. 2: Name two trig ratios that will allow us to calculate side b.
1) cos 409b
2) sin 509b
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A
B
C
Example 3: Determine side b
55º
b
8 cm
b = 8 tan 55°
b = 11.4 cm
b = 8 (1.428)
tan8
B b
tan 558b
opp
adj
SOHCAHTOA
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P
Q
R
12 cm
17 cm
Example 4: Determine the measure of P.
cos P = 0.70588
P = 45.1
P = cos–1(0.70588)
12cos17
P
adjacent
hypotenuse
SOHCAHTOA
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PQ
R
q
12 cm
Example 5: Determine the measure of side PR.
q(tan 35°) = 12
q = 17.1cm
12tan 35q
12tan 35
q
120.7007
q
35
opp adjMethod 1
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PQ
R
q
12 cm
Example 6: Determine the measure of side PR.
q = 12(tan 55°)
q = 17.1cm
tan 5512q
35
oppadjMethod 2
Q = 90° – 35°
Q = 55°
55°
q = 12(1.428)
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Ex. 7: In PQR, Q = 90°.
a) Find sin R if PR = 8 cm and PQ = 4 cm. R
P Q4 cm
8 cm
4sin8
R 12
b) Find cos R .
6.93cos8
R RQ2 = 82 – 42
RQ2 = 64 – 16
RQ2 = 48
48RQ cos 0.87R
6.9RQ 30R