Law of Sines and Law of Cosines What are all the ways we can solve Right Triangles?
What about nonright triangles?
Law of Sines
B c
a C
A
b
Law of Cosines
B c
A
a C
b
Use the law of sines... Find the length of b.
A b
108 o 33o
C
B
24
Find B. A
23 45 C
35o
B
Find B A
22 48o
63 B
C
Two people are walking toward each other on a path through the park. The path runs east and west. A hot air balloon in directly above the path between them. One of the walkers, a female, sees the balloon when looking east at an angle of elevation of 46o. The other walker, a male, sees the balloon looking west at an angle of elevation of 72o. If the walkers are 55 yards apart, how far is the balloon from the male observer?
Use the law of cosines...
Find c. B
29 c
41o 13
C
A
Find A A
6
9
B
14
C
Find C. C
29 A
101 o B
24
To Summarize... List all the methods we have for solving each type of triangle.
Right Triangles
NonRight Triangles
nes
d
si Co
n es a Sin
W k c i u Q of
Law
e t i r
Pick one of the questions below and answer using complete sentences in 60 words or less. a. What is the law of sines and how do you use it to solve problems? b. What is the law of cosines and how do you use it to solve problems? c. Compare the law of sines and cosines and describe when you would use one over the other. d. Will the law of sines and cosines work for right triangles? Explain including an example.
HW Questions AC #4
A clothing company wants to print the face of the Statue of Liberty on a Tshirt. The length of the face from the top of the forehead to the chin is 17 feet and the width of the face is 10 ft. Given that a medium sized Tshirt has a length of 29 in and a width of 20 in, what dimensions of the face are needed to produce a scaled version that will fit on the Tshirt? A) What shape would you use to model the face of the statue? B) Knowing that the maximum width of the tshirt is 20 inches, what scale factor is needed to make the width of the face fit on the shirt? C) What scale factor should be used to scale the length of the face? Explain your reasoning. D) Using the scale factor identified in part (c), what is the scaled length of the face? Will it fit on the shirt? E) Identify the scale factor you would use to ensure that the face of the statue is proportional and would fit on the tshirt. Identify the dimensions of the face that will be printed on the shirt. F) The tshirt company wants the width of the face to be no smaller than 10 inches. What scale factors could be used to create a scaled version of the face that meets this requirement? G) If it costs the company $0.005 for each square inch of print on a shirt, what is the maximum and minimum costs for printing the face of the Statue of Liberty on one t shirt?
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