Download Unit O Student Success Sheet (SSS)

Unit O Student Success Sheet (SSS)
Right Triangle Trigonometry (sections 4.3, 4.8)
Standards: Geom 19.0, Geom 20.0, Trig 7.0, Trig 8.0, Trig 12.0
Segerstrom High School -- Math Analysis Honors
Reminders:

Practice Problems (PQ & PT) are completed in spiral bound
notebook only.

All pages in spiral notebook should be labeled accordingly:
Name: _____________________________________
Unit ______ Concept ______ - (title of assignment)
Period: __________
Examples:
Unit O Concept 1 – Practice Quiz
Unit O Concept 1-4 – Practice Test
Thinkbinder Study Group: www.bit.ly/ChatUnitO

“Success is not the key to
happiness. Happiness is
the key to success. If you
love what you are doing,
you will be successful.
– Herman Cain
Website with all video links and resources:
kirchmathanalysis.blogspot.com

Edmodo Group Codes for class communication:
http://bit.ly/edmodo2013
Concept
#
1
2
3
4
5
6
7
8
9
10
evaluate angles in degrees or radians on a calculator
Mandatory
Practice
Practice quiz 1
finding angles on a calculator using inverse trig functions
Practice quiz 2
solving basic trig equations with non-exact answers
Practice quiz 3
finding all six trig ratios given point on terminal side
Practice quiz 4
Page 294 #5-12
finding all six trig ratios when given one trig ratio (must draw
right triangle)
using SOHCAHTOA to find missing pieces of right triangles
(given 2 sides, given angle and side)
using the 45-45-90 triangle
Practice quiz 5
Page 284 #9-16
Practice quiz 6
Page 284 #1-8; page 337 #1-10
using the 30-60-90 triangle
Practice quiz 8
solving basic right triangle word problems
Practice quiz 9
solving angle of elevation and depression word problems
Practice quiz 10
What we will be learning…
Optional Extra practice
from textbook
Page 275 #51-68; page 285 #57-62
Page 327 #1-9; page 328 #15-20
Practice quiz 7
Page 286 #69-76
Page 266 #59-64; Page 286 #77-84;
page 337 #17-32
This Unit is all about our favorite type of triangles: RIGHT TRIANGLES! There are lot of special relationships that only exist when a triangle has a RIGHT ANGLE, so
these triangles are super cool!
We will start with basic use of the trig functions on our calculator, both regular trig functions and INVERSE trig functions. Hopefully the word INVERSE means a lot
A trig function and an inverse trig function will “undo” each other and will have the same relationships
that all other inverses have numerically, algebraically, and graphically.
We will review our basic ratios of SOHCAHTOA that we learned in geometry, and see how those ratios apply to the unit circle ratios we looked at in Unit J. Putting
all of our knowledge together, including the PYTHAGOREAN THEOREM, we will solve right triangles – meaning to find ALL MISSING SIDES and ALL
MISSING ANGLES. Two special triangles exist that we will also solve, but we will be able to solve them using patterns instead of by using calculations.
more to you now than it used to!
Lastly, we will explore applications of right triangles, starting with the use of the PYTHAOGREAN THEOREM, and then using angles of elevation and depression.
It is most important to remember that angles of elevation always go UP from a
horizontal and angles of depression always go DOWN from a
horizontal.
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
evaluate angles in degrees or radians on a calculator
To use the reciprocal trig functions, we must do this:
CSC (cosecant) =
SEC (secant) =
COT (cotangent) =
We have TWO modes that our calculator can be in when dealing with trigonometry: DEGREES or RADIANS.
**You must make sure your calculator is in the mode you want it to be!!!
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
finding angles on a calculator using inverse trig functions
x+3 = 5
How would you get rid of the 3? Why does that work?
sin(x)=.7845
√
How do you get rid of the cube root? Why does that
work?
sin(x) =___: use sin-1(x) to solve
How do you get rid of the
cos(x) =___: use cos-1(x) to solve
Why does that work?
How do you get rid of the sin? Why does that work?
tan(x) =___: use tan-1(x) to solve
If your calculator is in DEGREE MODE, the answer they give you will be in DEGREES!
If your calculator is in RADIAN MODE, the answer they give you will be in RADIANS!
*My tip: Leave calculator in degree mode, and just CONVERT answers to radians at the end as necessary*
WHAT IS  ??? It is the Greek letter for THETA, and it is a variable
(just like “x”) that is commonly used in trigonometry!
These problems ask for the answers for one revolution of the Unit Circle. However, your calculator only gives you ONE answer.
You need to do two things:
1.
Make sure that answer is within one revolution of the Unit Circle example: sin(x)
= -.876. The calculator will tell you the answer is -61.16o. That is not within one revolution. Find a coterminal angle by
adding 360o to find that 298.84o is the real angle the calculator is talking about.
2.
Find the second answer using reference angles.
298.84o has a reference angle of 61.16o
(found by using 360-298.84). Because the problem was sin(x) = -.876, our two answers will lie in the two quadrants where
sine is negative. These quadrants are III and IV. 298.84o is in Quadrant IV, so we just have to find the angle in Quadrant III
that has a reference angle of 61.16o. We do this by taking 180o and adding 61.16o to it, giving us 241.16o as our second
answer.
Quadrants
1st answer
2nd answer
Quadrants
1st answer
2nd answer
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
solving basic trig equations with non-exact answers
Let’s take this one step further and solve trig equation where we have to do a little algebra
first…nothing from concept 2 changes!
Simplified equation
Quadrants
Answer #1
Answer #2
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
finding all six trig ratios given point on terminal side
y represents the opposite
Using the Pythagorean theorem, we know that
side
x represents the adjacent
side
r represents the hypotenuse
Sine:
Cosine:
Tangent:
sin
Cosecant:
cos
Secant:
tan
Cotangent:
csc
sec
cot
Example: Find all six trig functions given that a point on the terminal side of the angle is (-3,-4)
In this problem, x=-3 and y=-4
sin = -4/5
csc = -5/4
Using Pythagorean Theorem, r=5
cos = -3/5
sec = -5/3
Because the terminal side is in Quadrant III, only
tangent and cotangent should have positive values.
tan = 4/3
cot = 3/4
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
x= ______ y= _______ r= ______
Quadrant: ___; cos is + / -
x= ______ y= _______ r= ______
Quadrant: ___; sin is + / -
x= ______ y= _______ r= ______
x= ______ y= _______ r= ______
Quadrant: ___; csc is + / -
Quadrant: ___; tan is + / -
x= ______ y= _______ r= ______
x= ______ y= _______ r= ______
Quadrant: ___; cos is + / -
Quadrant: ___; cot is + / -
x= ______ y= _______ r= ______
x= ______ y= _______ r= ______
Quadrant: ___; sin is + / -
Quadrant: ___; sec is + / -
x= ______ y= _______ r= ______
For extra practice, find ALL SIX trig functions
for these problems!
Quadrant: ___; sin is + / -
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
finding all six trig ratios when given one trig ratio (must draw right triangle)
1.
2.
3.
4.
Take the trig function you are given and draw a Quadrant I right triangle labeled appropriately.
Find the missing side of the triangle.
Use the given information to find the requested trig ratio.
**Find all trig ratios for great practice!
sec =hyp/adj or r/x
242 + y2 = 252
2
y =49
y=7
cos= x/r = 24/25
sin = y/r = 7/25
tan = y/x = 7/24
csc= r/y = 25/7
cot = x/y = 24/7
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
using SOHCAHTOA to find missing pieces of right triangles (given 2 sides, given angle and side)
To SOLVE a right triangle, it means to find ALL MISSING SIDES and ALL MISSING ANGLES.
Angles are labeled with CAPITAL letters
Sides are labeled with LOWERCASE letters
Sides and angles correspond with each other because
they are ACROSS from each other.
C is the right angle…always!
Just for fun (to the tune of “We Will Rock You”:
Pythagorean Theorem goes with right triangles
Hypotenuse is across from the right angles
Legs are “a” and “b”
Hypotenuse “c”
Plug the numbers in and see how easy it can be!
Example: b=11, a= 7
Use the Pythagorean Theorem and Inverse Trig Functions to solve!
Note:
*Never use a rounded value in the middle of a problem unless there are no other options left!
We must find c, A, and B. Let’s start with c…
72 + 112 = c2  c = √
 13.0
(always check to make sure it doesn’t simplify; GIVE BOTH EXACT RADICAL AND APPROXIMATION)
o
-1
tanA=7/11  tan (7/11) = 32.5
o
tanB=11/7  tan-1(11/7) = 57.5
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
using the 30-60-90 triangle AND using the 45-45-90 triangle
See answers to all SSS examples above + 10 more examples to try of each type in the turquoise box of the blog.
Label each side according to the
pattern – n, n, n√
Solve for “n” first, and then find all
the missing sides.
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
Label each side according to
the pattern – n, 2n, n√
Solve for “n” first, and then find
all the missing sides.
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
Combining the Two…
Directions: Find the missing values.
Access PQ7-8 worksheet on
the blog for triangle
pictures.
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
solving basic right triangle word problems
One of the most common formulas used with right triangles is the Pythagorean Theorem!
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
solving angle of elevation and depression word problems
Angles are sometimes measured in DEGREES and MINUTES (and sometimes SECONDS!), instead of giving a decimal
approximation. This is similar to how latitute and longitude values are labeled.
Example: 36o4’ is 36 degrees, 4 minutes.
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
3a) A man at ground level measures the angle of elevation to the top of a building to be 67 o. If, at this point, he is 15
feet away from the building, what is the height of the building?
3b) The same man now stands atop a building. He measures the angle of elevation to the building across the street to be
27o and the angle of depression (to the base of the building across the street) to be 31 o. If the two buildings are 50 feet
apart, how tall is the taller building?
5) From a point 120 feet from the base of a church, the angles of elevation of the top of the building and the top of a
cross are 38o and 43o, respectively.
a) Find the height of the cross. (The ground is flat).
b) Find the height of the building (not including the cross)
6) A man is just about to ski down a steep mountain. He estimates the angle of depression from where he is now to the
flag at the bottom of the course to be 24o . He knows that he is 800 feet higher than the base of the course. How long is
the path that he will ski? (Round to the nearest foot).
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
There is always the possibility that there is an error in the answer key (WE ALL MAKE MISTAKES SOMETIMES!) If you
believe you have found an error, please submit the “Submit an Error” form that you’ll find on the right hand side of the
kirchmathanalysis.blogspot.com site. Mrs. Kirch will double-check and verify.
THANK YOU FOR YOUR HARD WORK AND ATTENTION TO DETAIL!
Unit O Practice Quiz 1
Unit O Practice Quiz 2
Unit O Practice Quiz 3
Unit O Practice Quiz 4
Unit O Practice Quiz 5
Unit O Practice Quiz 6
Unit O Practice Quiz 7-8
See KEY AT END OF DOCUMENT on blog
Unit O Practice Quiz 9
1.
2.
7.4 in
9.4 miles
3.
4.
4 feet
NO (does not satisfy Pyth Thm)
Unit O Practice Quiz 10
1.
2.
3.
4.
21.8 degrees
14.3 meters
26.6 degrees
101,278.3 feet
5.
6.
7.
37.1 yards
.2 miles
81.5 degrees
8. No, 6.3 feet
9. 24.8 meters
10. 18.0 meters
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
Unit O Practice Test
Use the same directions from the PQ problems for each concept to solve these in
order to prepare for the test. Answer key is posted online only at
kirchmathanalysis.blogspot.com
Concept 1
Concept 2
Concept 3
Concept 4
Concept 5
Concept 6
Concept 7-8
Finish the rest of the PQ problems
1.
2.
Concept 9
3.
4.
To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south
and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
A baseball diamond is a square with sides of 90 feet. What is the shortest distance, to the nearest tenth of a foot, between
first base and third base?
A suitcase measures 24 inches long and 18 inches high. What is the diagonal length of the suitcase to the nearest tenth of a
foot?
In a computer catalog, a computer monitor is listed as being 19 inches. This distance is the diagonal distance across the
screen. If the screen measures 10 inches in height, what is the actual width of the screen to the nearest inch?
© Crystal Kirch 2011
---Unit O Student Success Sheet--- Right Triangle Trigonometry (sections 4.3, 4.8)---Math Analysis Honors---
Concept
10
Unit Circle values/angles
(Unit N Concept 8-9)
Video answer key:
Review
Solving 3-variable
systems
(Unit J Concept 3)
© Crystal Kirch 2011