Unit 8

NAME __________________________
INTRO TO TRIG
UNIT 8
LAW OF SINES/ LAW OF COSINES
DATE PAGE TOPIC HOMEWORK
2/25 2 Finding area of a non-right triangle Pg 829 #1, 6, 11, 20
2/26 3 Law of Sines Pg 834 # 3, 9, 10, 15
2/27 X More law of Sines
NO Homework!
QUIZ
2/28 4 Law of Cosines to find a side Pg 819 # 4, 11, 12, 14
3/1 5 Law of Cosines to find an angle Pg 824 # 3, 6, 8, 9
3/4 X QUIZ
NO Homework!
Make Foldable
3/5 6 Law of Sines/Cosines Mix up Pg 850 #1, 2, 3
3/6 7 Word Problems with LOS and LOC Pg 850 #7, 9, 10
3/7 8 Forces Pg 844 #1, 4, 6
3/8 X More practice with Forces P 844 # 7, 8
3/11 QUIZ
Finish Review
Review Sheet
3/12 Review STUDY FOR TEST
3/13 TEST
1

Area of a Triangle
Use the formula below when you are trying to find the area of a triangle and you don't know the height of the
triangle.
B
Area of a Triangle:
c
a
A
b
C
Examples:
1.) Find the area of triangle ABC if c=8, a=6 and angle B=30 o
2.) Find the area of an equilateral triangle with one side equal to 4.
3.) The area of a parallelogram is 20. The measures of the sides are 8 and 5. What is the
measure of each angle?
2

LAW OF SINES
You use the Law of Sines when you know TWO ANGLES AND ONE SIDE OPPOSITE THEM or when you know
TWO SIDES AND ONE ANGLE OPPOSITE THEM.
B
LAW OF SINES:
c
a
A
b
C
Examples:
1.) Find b if a=10, angle A=30 o , angle B=50 o
2.) Find c if sin A =1/3, and sin C=1/4 and a=12
3.) Find to the nearest tenth, the length of one of the congruent sides of an isosceles triangle if the measure
of the base is 42cm and the vertex angle is 65.5 o .
4.) Find

LAW OF COSINES
FINDING A MISSING SIDE
You use the Law of Cosines when you have TWO SIDES AND THE INCLUDED ANGLE in a non-right
triangle.
B
LAW OF COSINES:
c
a
A
b
C
1.) Find b if c=6, a=4 and Cos B=1/16
2.) Find t if s=12, r=11 and T=120 o
3.) Find d if a=6, b= 3 3 , D=30 o
4

Recall the Law of Cosines:
LAW OF COSINES
FINDING A MISSING ANGLE
Examples solving for angles:
1.) Find angle P if m=3, n=4, and p=2
2.) Find angle Y if x=3, y=4, and z=5
3.) Find CosR in triangle ROB if r=20, o=15, b=16.
5

When do I use which Law????
General rule of thumb:
Use law of cosines when...
Use law of sines when...
USE YOUR FOLDABLE!
1.) a.) In DABC, a = 14 cm, b = 9 cm, c = 6 cm. Find angle A.
b.) Find Angle B.
c.) Find Angle C.
2.) Find all missing sides and all missing angles in the following triangle:
In triangle ABC, m

Angle Of Elevation
Angle of Depression
A signal tower has two lights that are 30 feet apart, one directly above the other. From a boat, the
angle of elevation of the lower light is measured to be 19 degrees and the angle of elevation of the
upper light is measured to be 32 degrees.
a.) Draw a picture:
b.) Find, to the nearest foot the distance from the boat to the lower light.
c.) Find, to the nearest foot, the distance from the boat to the foot of the tower.
4.) From the top of a barn 25 feet tall, you see a cat on the ground. The angle of depression to the
cat is 40 o . How many feet, to the nearest foot, must the cat walk to reach the barn?
7

If two forces act to push or
pull on an object in the same
direction, the effect is that of
a single force equal to the
sum of the two forces.
Ex.
FORCES
If two forces act to push or
pull on an object in opposite
directions, the effect is that of
a single force equal to the
difference between the applied
forces.
Ex.
If two forces act to push or pull in
directions that form an angle other
than straight, the effect is that of a
single force acting in a direction in
the interior if the angle between
them.
Ex.
Examples:
1.) Forces of 25 and 15 act on a body so the angle between them is 75 o . Find the magnitude of the
resultant.
2.) Two applied forces act at angles of 35 o and 47 o with the resultant which is 143lbs.
Find the larger force.
3.) Find to the nearest degree the measure of the angle between two forces of 9 and 11
pounds if the resultant is 14.
8