Geometry
Chapter 7: RIGHT TRIANGLE AND TRIGONOMETRY
Day
Topic
Name____________________________________
Period__________________________________
Assignment
Score
1
7.1 Apply the Pythagorean Theorem.
What is the Pythagorean Theorem? 𝑎2 + 𝑏 2 = 𝑐 2 , where a, b are the legs and c is the hypotenuse.
Pythagorean triple? It is a right triangle that has 3,4,5 or 5,12,13 or 8,15,17 or 7,24,25 and their various multiples.
7.1 Workbook.
1-38 all
p.439 mixed
review 39-50
7.2 Workbook.
1-25 all
p.447 mixed
review 46-52
/4
2
7.2 Use the converse of the Pythagorean Theorem.
How do you know if the triangle is a right triangle? Use the Pythagorean formula and see if the right side equals the left
side. Remember that the longest side is the hypotenuse and takes on the letter c.
How do you tell if the triangle is an acute triangle? Use the Pythagorean formula with 𝑎2 + 𝑏 2 > 𝑐 2.
How do you tell if the triangle is an obtuse triangle? Use the Pythagorean formula with 𝑎2 + 𝑏 2 < 𝑐 2 .
3
7.4 Special right Triangles.
Create a 45° − 45° − 90° triangle. Let 1 be the side of the leg and use the Pythagorean theorem to find the hypotenuse.
Suppose the leg is 3 what is the hypotenuse? Suppose the leg is x what is the hypotenuse?
Create a 30° − 60° − 90° triangle. Let 1 be the side of the leg opposite the 30° and 2 (double)be the length of the
hypotenuse. Use the Pythagorean theorem to find the length of the side opposite the 60⁰ angle. Let 3 be the side of the
leg opposite the 30° and 6 (double) be the length of the hypotenuse. Use the Pythagorean theorem to find the length of
the side opposite the 60⁰ angle. Let x be the side of the leg opposite the 30° and 2x (double) be the length of the
hypotenuse. Use the Pythagorean theorem to find the length of the side opposite the 60⁰ angle.
7.4 Workbook.
1-25 all
p.464 mixed
review 36-44
/4
4
7.5 Apply the tangent ratio.
What is a trigonometric ratio? It is a ratio of the lengths of two sides in a right triangle.
What is a tangent? It is the ratio of the lengths of the legs in a right triangle that is a constant for a given angle measure.
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑒𝑔 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑜𝑓 𝑎𝑛𝑔𝑙𝑒 𝐴
tan 𝐴 =
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑒𝑔 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐴
7.5 Workbook.
1-27 all
p.472 mixed
review 3-47
/4
5
7.6 Apply the sine and cosine ratios.
The sine and cosine ratios are trigonometric ratios for acute angles that involve the lengths of a leg and the hypotenuse
of a right triangle.
7.6 Workbook.
1-28 all
p.480 mixed
review 42-48
/4
sin 𝐴 =
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑒𝑔 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑜𝑓 𝑎𝑛𝑔𝑙𝑒 𝐴
𝑙𝑒𝑔𝑛𝑡ℎ 𝑜𝑓ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
cos 𝐴 =
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑒𝑔 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐴
𝑙𝑒𝑔𝑛𝑡ℎ 𝑜𝑓ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
What is an angle of elevation? If you look up at an object, it is the angle your line of sight makes with a horizontal line.
What is an angle of depression? If you look down at an object, it is the angle your line of sight makes with the horizon.
What is the relationship between the angle of elevation and the angle of depression? Yes, they are congruent by
alternate interior angles.
/4
6
7.7 Solve right triangles.
What does it mean to solve a right triangle? It means to find the measures of all its sides and angles.
Use inverse trigonometric ratios to solve the triangle:
𝑎
𝑎
If tan 𝜃 = 𝑏 , then tan−1 𝑏 = 𝜃.
𝑎
7.7 Workbook .
1-27 all
p.489 mixed
review 43-48
/4
𝑎
If sin 𝜃 = 𝑏 , then sin−1 𝑏 = 𝜃.
𝑎
𝑎
If cos 𝜃 = 𝑏 , then cos−1 𝑏 = 𝜃.
7
Chapter 7 review.
Chapter 7 practice test.
pp. 494-497 pp. 282-285
/4
1-33 all
1-29 all
p. 498 1-17 all
Total Total points /28
/36
8
Chapter 7 Exam. You have one shot at it so give it your very best effort.
I still have questions about:
Homework Rubric
Score: 0
I didn’t do the assignment.
Score: 1
I did at least 50% of the
assignment.
I did the assignment by the
end of the chapter.
I showed some work.
I checked some of my
answers with similar
problems in the textbook or
online book.
If I had questions, I didn’t
seek help.
Score: 2
I did at least 75% of the
assignment.
I did the assignment by the
end of the chapter.
I showed most of my work.
I checked most of my
answers with similar
problems in the textbook or
online book.
If I had questions, I sought
help most of the time.
Where can I get help?
My classmates. Form a study group! Get phone numbers or emails so that
you can phone a friend when you are in the hot seat.
My teacher. I’m in the Math Department Office (E200) from 7:00-7:30am
and 1:50-2:30 every day. I also have 3rd period planning so you can get help
from me. I have advisory in F203 and you are encouraged to come and get
help from me during travel days.
Free Tutoring. Let me know if you need a tutor.
Score: 3
I did 100% of the assignment.
Score: 4
I did 100% of the assignment.
I did the assignment on time.
I did the assignment on time.
I showed all my work.
I checked all my answers with
similar problems in the
textbook or online book.
I showed all my work.
I checked all my answers with
similar problems in the
textbook or online book.
If I had questions, I sought help
all the time.
If I had questions, I sought
help all the time.
I taught the material to a
classmate, friend, or adult.
My parents or other adults. They are smarter than you think! Besides, it
creates good bonding time.
Textbook and its tutorial website, www.classzone.com. Select Little:
Geometry 2007, then choose code (ask me). Go to the online book at the
bottom of the screen and choose the desired chapter. There are lots of
practice problems here.
The World Wide Web. Check out the documents and links at
http://teacher.edmonds.wednet.edu/edmondswoodway/swahbeh