Honors Pre-Calculus
Chapter 7
Application of Trig Functions
Mrs. Boddy
Chapter 7 – Assignment Guide
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R:
p. 536 1,5,9,21,25,29,33,43,45,51,55,59,61
F:
p. 547 3,9,29,31,33,43
M:
p. 555 1,5,13,17,25,29
T:
Review
W:
Ch 7 Quiz
Honors Pre-Calculus
7.1
Right Triangle Trigonometry
Learning Targets: Students will be able to solve right triangles and solve applied problems using right triangle
trigonometry.
.

SOH-CAH-TOA
c
b


a
sine =
opposite leg
hypotenuse
adjacent leg
hypotenuse
cosine =
tangent =
opposite leg
adjacent leg
cosecant =
secant =
hypotenuse
opposite leg
hypotenuse
adjacent leg
cotangent =
adjacent leg
opposite leg
sin  
a
c
sin  
b
c
cos  
b
c
cos  
a
c
tan  
a
b
tan  
b
a
csc  
c
a
csc  
c
b
csc 
1
sin
sec  
c
b
sec  
c
a
sec 
1
cos
cot  
b
a
cot  
a
b
cot 
1
tan
THM: Cofunctions of complementary angles are equal.
Find the exact value of the six trigonometric functions of the angle  in the figure below.
8.

sin  
csc =
cos  
sec =
tan  
cot =
3
2
Solve the right triangle. (They give you 3 pieces, you find the other 3, and   90 )
28. a  6,   40
46. A ship is just offshore of New York City. A sighting is taken of the Statue of Liberty, which is about 305
feet tall. If the angle of elevation to the top of the statue is 20 , how far is the ship from the base of the statue?
58. A security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. What angle of
depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the
wall?
60. A ship leaves the port of Miami with a bearing of S 80 E and a speed of 15 knots. After 1 hour, the ship
turns 90 toward the south. After 2 hours, maintaining the same speed, what is the bearing to the ship from the
port?
Honors Pre-Calculus
7.2
Law of Sines
Learning Targets: Students will be able solve SAA or ASA triangles and solve applied problems using the Law of
Sines.
Law of Sines – Used to solve non-right triangles where traditional trig would work.
Law of Sines is used when you are given the following information about a triangle:
A)
ASA
B)
AAS
C)
SSA – ambiguous case (we will not be doing this year)
Law of Sines:
a
b
c


sin  sin  sin 
OR
sin  sin  sin 


a
b
c
Triangle labels follow this pattern:
10. Solve for all missing parts, given that   50 ,   20 , a  3
34. The highest bridge in the world is the bridge over the Royal Gorge of the Arkansas River in Colorado.
Sighting to the same point at water level directly under the bridge are taken from each side of the 880 foot long
bridge. How high is the bridge?
Bridge
65.5
69.2
Height
40. The navigator of a ship at sea spots two lighthouses that she knows to be 3 miles apart along a straight
seashore. She determines that the angles formed between two line of sight observations of the lighthouses and
the line from the ship directly to shore are 15 and 35 .
Lighthouse A
Shore
15
35
ship
Lighthouse B
A)
How far is the ship from lighthouse A?
B)
How far is the ship from lighthouse B?
C)
How far is the ship from shore?
Honors Pre-Calculus
7.3
Law of Cosines
Learning Targets: Students will be able to solve SAS and SSS triangles and solve applied problems using the Law of
Cosines.
Remember, Law of Sines is used if you are given: AAS or ASA
If you are given SSS or SAS, then you use the Law of Cosines.
Law of Cosines:
To find side:
To find angle:
a 2  b 2  c 2  2bc cos A
cos A 
b2  c2  a 2
2bc
b 2  a 2  c 2  2ac cos B
cos B 
a 2  c2  b2
2ac
c 2  a 2  b 2  2ab cos C
cos C 
a 2  b2  c2
2ab
If SAS:
1. Find missing side by law of cosines
2. Find smallest angle by law of sines
3. Subtract 2 angles from 180
If SSS:
1. Find smallest angle by law of cosines
2. Find next smallest angle by law of sines
3. Subtract 2 angles from 180
10.
22.
a  2, c  1,  =10
a  4, b  3, c  6