Final Exam Project - Chapter 7: Law of Sine and Cosine
As a review, it is recommended that you complete & submit this assignment before taking the
exam.
Due Date: The original post is due by 11:59pm three (3) days before the Final Exam is due.
Replies are due by 11:59pm of the last day that the Final Exam is due.
INTRODUCTION
Project:
This project will enable you to explore various oblique triangles including the familiar right triangle. It
will give insight on the relationship between angles of a triangle and the corresponding opposite
sides.
ACTIVITY/PROCESS AND GRADING (TOTAL = 50 (40 + 5 + 5) POINTS)
You will submit your work to Final Exam Project forum in Blackboard. Only submit your work in one of
the following ways:
• Take a picture of your written project. Make sure it is readable. Upload the image to the discussion
forum.
• While working through this project, please save your work in a Word document at each step in order
to submit the completed file in its entirety. Make sure you answer all questions in complete
sentences.
• Upload the file to the discussion forum.
• To snip/crop & copy an image, pull up your image/photo on the screen:
o Mac: Use Command + Shift + 4, click and drag cursor across the part of the image that you
want to use. It will take a screenshot of your selected area and automatically save it to your
desktop.
o Windows: Go to Start Menu>>All Programs>>Accessories>>Snipping Tool. Drag the cursor
around the area that you want to capture. Name and save to your desktop.
This assignment is REQUIRED and will only be graded if resources and conclusion are part of the
project. The point values for each section are noted below with an additional 10 points for replies to
classmates. You are required to review at least two classmates’ projects and post a substantive reply to
each (5 points for each reply for up to a total of 10 points). “Good Job” or “I didn’t think of that” will not do.
You must post a follow-up question, an observation, make a suggestion, or apply some additional insight
to what your classmate has posted. It is NOT your place to point out or correct errors. If you find an error
that needs correcting, email your instructor for verification and the instructor will contact the student if your
observation is correct.
EXPLORING RATIOS: 10 Points
In the Word document, add a heading called Exploring Ratios. Write the answers for this section
under the heading. Continue to update your document as you continue through each section and
submit one document at the end of this project.
The Law of Sines is a relationship among angles of a triangle and their corresponding opposite
sides. This law states that the ratio of the sine of any of the interior angles of a triangle to the length
of the side opposite the angle is the same for all three interior angles. In other words,
sin 𝐴 sin 𝐵 sin 𝐶
=
=
𝑎
𝑏
𝑐
Final Exam Project - Chapter 7: Law of Sine and Cosine
As a review, it is recommended that you complete & submit this assignment before taking the
exam.
Due Date: The original post is due by 11:59pm three (3) days before the Final Exam is due.
Replies are due by 11:59pm of the last day that the Final Exam is due.
In the equation a, b, and c are the lengths of the sides that are opposite of their angles A, B, C.
In order to understand a ratio, let’s consider a ratio in everyday life. Determine how much one donut
costs if a dozen donuts costs $4.20. In order to answer this question we will use ratios. The
numerators will be the same units as well as the denominators. Our problem becomes $4.20/12 =
$x/1 and therefore, one donut costs $.35 cents. In the same way that this problem uses ratios, ratios
are used in trigonometry in the Law of Sines (notice both equations have fractions set equal to each
other).
1) Using ratios, determine how much 6 donuts cost. Notice that when the denominator increases,
the value of the unknown in the numerator increases. Now assume that donuts double in cost.
Change the ratio to show this. If the denominator of the known value is increased by a factor of
2, what happens to our unknown?
2) Setup and solve an everyday problem using ratios to solve it. Keeping the fraction you have
created, change one value on the side that has the unknown and solve the problem again.
3) As we change that one value, what happens to the unknown? Explain the various possibilities.
EXPLORING THE LAW OF SINES WITH KNOWLEDGE WE KNOW: 15 points
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To see this relationship, use the Wolfram Demonstrations Project website
(http://www.wolfram.com/).
Click on the “Try the Interactive CDF examples” link under Professional & Enterprise column on
the left of the page (http://www.wolfram.com/cdf/uses-examples/?fp=left). Note: You may need
to download the CDF player first. Scroll to the middle of the page & click on the red “Interact
Now: Get the free Wolfram CDF Player” button.
On the CDF Player page (http://www.wolfram.com/cdf-player/ or http://www.wolfram.com/cdfplayer/plugin/success.html?platform=WIN), click on “Explore demonstrations now” link at the
bottom left of the page.
Under the heading Wolfram Demonstrations Project, search for The Law of Sines and choose
The Law of Sines.
In Word, add a heading called Exploring the Law of Sines. Write the answers below. Submit
one document at the end of this project.
1) To begin with information we know, move the dot at B and C (to change the angles) so that A
becomes 90 degrees. Recall the value of sin (90) in order to get the triangle to look right. Draw
the resulting triangle and label the values for all other angles and sides. Use the Pythagorean
Theorem to verify that this triangle is a right triangle using values rounded to the hundredth digit.
Note: This may not be an exact match but it should be very close. Use the snipping tool and
capture this picture to place in Word. Add your algebraic work.
2) Keeping A equal to 90 degrees, increase α. Again draw the resulting triangle and label the
values for all other angles and sides. Use the Pythagorean Theorem to verify that this is a right
triangle using values rounded to the hundredth digit. Note: This may not be an exact match but it
should be very close. Use the snipping tool and capture this picture to place in Word. Add your
algebraic work.
3) Now change the angle of A so that it is not a right triangle. Draw the resulting triangle and label
the values for all other angles and sides. Use the Pythagorean Theorem to verify that is not a
Final Exam Project - Chapter 7: Law of Sine and Cosine
As a review, it is recommended that you complete & submit this assignment before taking the
exam.
Due Date: The original post is due by 11:59pm three (3) days before the Final Exam is due.
Replies are due by 11:59pm of the last day that the Final Exam is due.
right triangle using values rounded to the hundredth digit. Use the snipping tool and capture this
picture to place in Word. Add your algebraic work.
4) Use the Law of Sines to write the three equivalent ratios of your oblique triangle. Explain how
ratios are working in this problem as they did in the problems above. Use the snipping tool and
capture this picture to place in Word. Add your algebraic work.
EXPLORING THE LAW OF COSINES: 15 points
In Word, add a heading called Exploring the Law of Cosines and answer the questions below.
The Law of Cosines relates the three side lengths of a triangle with the cosine of one of its angles. If
this angle, call it A, is formed by sides b and c and the opposite side a, then according to the Law of
Cosines, 𝑎 + = 𝑏 + + 𝑐 + − 2𝑏𝑐 cos 𝐴. In the equation, a, b, and c are the lengths of the sides that are
opposite of their angles A, B, C.
•
•
To see this relationship, use the Wolfram Demonstrations Project website
(http://www.wolfram.com/).
Under the heading Wolfram Demonstrations Project, search for Law of Cosines and choose
Law of Cosines.
1) Let’s again start with something we know. Make angle A equal to 90 degrees. Recall the value of
cos (90) in order to get the triangle to look right. Draw the resulting triangle and label the values
for all other angles and sides except a. Using the Law of Cosines complete the algebra to find
the value for a. Since A = 90 degrees, in a complete sentence answer the question what familiar
formula does the Law of Cosines represent? Use the snipping tool to capture the picture and
place it in Word under the heading Exploring the Law of Cosines.
2) Make the angle A an obtuse or acute triangle. Draw the resulting triangle and label the values for
all other angles and sides except a. Using the Law of Cosines, complete the algebra to solve for
a. Does this value match the value of 𝛼 shown on the demonstration? Use the snipping tool to
capture the picture and place it in Word under the heading Exploring the Law of Cosines.
3) Create a real life example for your values. Add drawings or pictures to the significant landmarks
as well as the measurements. If needed, reference the internet or Chapter 7.2 of your textbook
for ideas.
CONCLUSION & RESOURCES
Write a summary (minimum of 3 sentences) of what you learned doing this project.
Remember to list any resources you used for this project including books and or internet sites.
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