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Youngstown City Schools
MATH: GEOMETRY
UNIT 2B: TRIGONOMETRY (6 WEEKS) 2013-2014
Synopsis: Students will study and expand upon the concept of trigonometry, starting with the connection
to similar triangles and ending with real life applications using the law of sines and cosines. Due to the
length of this unit, it will be broken into three sections with an assessment after each section.
STANDARDS
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to
definitions of trigonometric ratios for acute angles.
G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human
torso as a cylinder).*
G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per
cubic foot).*
G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints
or minimize cost; working with typographic grid systems based on ratios).*
G.SRT.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex
perpendicular to the opposite side.
G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
G.SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).
MATH PRACTICES
1. Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning
LITERACY STANDARDS
L.1
L.2
L.5
Learn to read mathematical text (including textbooks, articles, problems, problem explanations)
Communicate using correct mathematical terminology
Justify orally and in writing mathematical reasoning
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YCS MATH GEOMETRY: UNIT 2B Trigonometry
2013-2014
1
MOTIVATION
1. Show the you tube video on building clinometers
TEACHER NOTES
http://www.youtube.com/watch?v=CsNbfxDQnYM. Explain to students that they will be building their
own clinometers and using them to calculate heights of objects later in the unit. (G.SRT.8, MP.2,
MP.4, MP.5, MP.7, L.2)
2. Discuss uses of trigonometry in real life: surveyors and civil engineers use it to calculate distances
and angles; carpenters use it to find missing lengths when building a house; electrical engineers who
test speakers use it to achieve maximum performance from their speakers; manufacturing products
technologies use it to determine the important angles of manufacturing tools; it is used in geography
and navigation by sailors to determine their positions when they were in the middle of the sea;
astronomers use it to calculate the position of the planets; and the geographical concept of latitude
and longitude are also applications of trigonometry. (G.SRT.8, MP.4, L.2)
3. Preview expectations for end of Unit
4. Have students set both personal and academic goals for this Unit or grading period.
TEACHING-LEARNING
Vocabulary
Sine
Cosine
Clinometers
TEACHER NOTES
Trigonometry
Radicals
Altitude
Opposite side
Adjacent side
Hypotenuse
Leg
Complementary angle
Tangent
1. Start the introduction to trigonometry with the activity in the textbook on page 365, then extend it to
include angle C also. After this is completed, explain to the students the decimal representation for
cos 22° is calculated by taking a right triangle with a 22° angle, measuring the side adjacent to the
angle and the hypotenuse, creating a ratio of
, and divide to get the decimal
approximation. Every time you take a right triangle with a 22° angle and set up this ratio, it will
always give the same result regardless of the length of the sides because the triangles are similar.
This is a great deal of work, so mathematicians made a trig table to make calculations with angles
and sides of triangles easier. Show students trig table on the web site:
http://www.classzone.com/cz/books/pre_alg/resources/pdfs/formulas_and_tables/palg_table_of_trig_
ratios.pdf. Now, of course, this is programmed into calculators and trig tables are no longer needed.
(G.SRT.6, MP.2, MP.4, MP.8, L.2)
2. Review the terminology using pictures of right triangles: trigonometry, side (leg) adjacent, side (leg)
opposite, hypotenuse, leg, complementary angles. (G.SRT.6, MP.4, L.2)
3. Student activity: draw right triangle ABC with AC perpendicular to AB. Have students fill in the table
and explain the relationship between angle C and angle B: (G.SRT.6, MP.2, MP.4, MP.7, L.2, L.5)
Angle
B
C
Side opposite
Side adjacent
Hypotenuse
4. Activity: Solve the following using similar triangles, in ∆ABC, AC is perpendicular to BC and in
∆RST,RS is perpendicular to ST.
1. ∆ABC
6/30/2013
∆RST, BC = 3, AB = 5, RS = 15, find TS (ans. 9)
YCS MATH GEOMETRY: UNIT 2B Trigonometry
2013-2014
2
TEACHING-LEARNING
2. ∆ABC
TEACHER NOTES
∆RST, AC = 9, AB = 14, RS = 4, find RT (ans. 2.6)
After students solve these problems, state the definition of sine, cosine and tangent ratios. Then, ask
them if there is an easier method of solving the above problems. Use the trig tables to show them for
the first problem the left hand side (ratio) is the same as cos 53° and the problem can be solved very
simply by multiplying cos 53° by 15 to find TS. Likewise, the left hand side (ratio) of the second
problem is the same as sin 40° (looking at the trig tables), so this problem can be solved by
multiplying 40° by 4 to find RT. (G.SRT.6, MP.2, MP.3, MP.4, MP.6, MP,8, L.2, L.5)
5. Show students how to use the calculator when working with trig functions. Make sure the calculator
is in the degree mode before beginning. Compare these values to the values on the trig tables and
discuss similarities and differences. Have students fill in the chart below:
Angle
50
40
30
60
70
20
25
65
Cosine
Sine
Discuss the pairs of angles and their relationship to each other. Then question students about the
values of the cosine and sine. They should reach the conjecture that the cosine of an angle is equal
to the sine of its complement and the sine of an angle is equal to the cosine of the complement.
Discuss the reasoning for this with diagrams of right triangles. (G.SRT.6, G.SRT.7, MP.2, MP.3,
MP.4, MP.8, L.2, L.5)
6. Reinforce with the following examples: (G.SRT.6, G.SRT.8, MP.1, MP.4, MP.5, MP.6, MP.8, L.1,
L.2)
a) A wire attached to a pole makes a 63° with the ground and is 12′ from the base of the pole.
Find the height of the pole. (Ans. 23.5′)
b) A roof truss is in the shape of an isosceles triangle. The base angles are 25° and the equal
sides are 10′ each. Find the height of the truss (triangle). (Ans. 4.2′)
c) A road is going up a mountain and makes a 28° angle with the horizontal. How high would you
have to rise in going 250 meters up the road? (Ans. 11.7 meters)
d) A 10 foot log is leaning against a barn and makes a 54° angle with the ground. How far is the
log from the foot of the barn? (Ans. 5.9 feet)
e) A wire 25 ft. long is supporting an 18 ft. pole. Find the angle formed by the wire and the pole.
(Ans. 43.9°)
7. Reinforce with Kuta worksheets (G.SRT.6, G.SRT.8, MP.1, MP.4, MP.5, MP.6, MP.8, L.1, L.2)
1. Trigonometric ratios http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/9Trigonometric%20Ratios.pdf
2. Solving for sides of right triangles
http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/9Solving%20Right%20Triangles.pdf
3. Solving for angles of right triangles
http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Trigonometry%20to%20Fin
d%20Angle%20Measures.pdf
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YCS MATH GEOMETRY: UNIT 2B Trigonometry
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3
TEACHING-LEARNING
8. To reinforce real-life problems, use section 7-5 in the textbook. Make sure the angles of elevation
TEACHER NOTES
and depression are discussed which are also found in chapter 7. (G.SRT.8, MP.1, MP.4, MP.5,
MP.6, MP.8, L.1, L.2)
9. Before starting the clinometer activity, revisit step 1 of the motivational activity. Create the
clinometers using the following web site and the video in the motivational activity:
http://repository-intralibrary.leedsmet.ac.uk/open_virtual_file_path/i1442n87724t/shapestheod2_clinometer.pdf
Pass out worksheet #1 (attached on page 12) which is the clinometers project. Have
students complete the project. (G.SRT.8, MP.1, MP.4, MP.5, MP.6, MP.8, L.1, L.2)
10. Review simplifying radicals. Students should be able to simplify the following radicals before
working on 30-60-90 and 45-45-90 triangles:
,
,
,
,
,
,
11. To begin working on the 45-45-90 triangles (isosceles right triangles) and the relationship between
the sides, have students derive the relationship using the Pythagorean theorem and letting the two
equal sides be one. If they don’t see the relationship after one example, have them do several
more, letting the equal sides be 3, 4, etc. To reinforce, work a few problems using the Kuta
worksheet problems 1- 6: (G.SRT.8, MP.4, MP.7, MP.8, L.2)
http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/8Special%20Right%20Triangles.pdf
12. Discovery activity with equilateral triangles that have a perpendicular bisector (altitude):
Ask students if they want to work with fractions or whole numbers. Of course they are going to say
whole numbers, so call the sides of the equilateral triangle 2x. Then have the students use the
Pythagorean theorem to find the length of the perpendicular bisector, leaving the answer in simple
radical form. Discuss the angle measures (30-60-90) and the relationship between the sides. To
reinforce have students work on the following: (G.SRT.8, MP.1, MP.2, MP.4, MP.6, MP.7, MP.8,
L.1, L.2)
a) A piece of tile is in the shape of an isosceles trapezoid having base angles of 60°, and bases
10 and 16. Find the height and legs of the trapezoid. (Ans. Height = 3
and legs are 6
each)
b) A telephone pole is 24 ft. high with a guy wire attached to the top of it. The guy wire makes a
60° angle with the ground. How far is the wire from the base of the pole? (Ans. 8
)
c)
A
B
D
In ∆ADC, AD is perpendicular to DC
and DB is perpendicular to AC. <C =
300 and DC is 12, find the remaining
sides, angles, and altitude of ∆ADC
C
(Ans. BC = 6 , DB = 6, AD = 4 , AB=
2 , AC = 8 , <BDC = 60, <BDA = 30,
<A = 60)
d) http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/8Special%20Right%20Triangles.pdf problems 7-18
13. Discuss example #11 on page 360 in the textbook and then have students create their own
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TEACHING-LEARNING
TEACHER NOTES
problems using 45-45-90 or 30-60-90 relationships. (G.SRT.8, MP.1, MP.2, MP.4, MP.8, L.1, L.2)
Have students take test #1 on standards G.SRT.6, G.SRT.7, and G.SRT.8
14. Geometry is found in everyday life. To assist students with this, find some objects that are
represented by geometric shapes and create problems from them. Listed below are two examples
of this: (G.MG.1, MP.1, MP.4, MP.5, MP.6, MP.7, MP.8, L.2)
a) Using a rectangular table top with dimensions 10 in. by 20 in. Find the length of the diagonal
and the angle between the diagonal and the 20 in. side. (Ans. 10 , 26.6°)
b) TV’s are measured by the diagonal. What size TV should you purchase if your cabinet is 40 in.
and the angle between the diagonal and the 40 in. side is 29°? (Ans. 45 in. TV)
15. Area is a concept that is also prevalent in our lives today, using it to purchase carpet, paint a room,
and seed a yard. Review the area of a triangle (Area = ½ b*h) and later, we will extend it to
trigonometry. Start with the following examples: (G.MG.1, MP.1, MP.2, MP.4, MP.5, MP.6, MP.8,
L.1, L.2)
a) Find the area of a triangular entrance way that needs to be tiled. The entrance way is a right
triangle with hypotenuse 8 ft. and length of one side 6 ft. (Ans. 6
).
b) A company is building signs in the shape of right triangles as shown below. To prepare to paint
them, they need to know the area of the triangles. Find the area.
DB is perpendicular to AC, <A =
28°. <C = 70°, and AD is 10 in.
Find the area. (Ans. 24.6 sq. in.)
D
A
c.
B
C
<ADC is a right angle, DB is
perpendicular to AC, <A = 35°.
and AD is 15 in. Find the area.
D
(Ans. 78.75 sq. in.)
A
B
C
16. Population density is an important concept used by statisticians: Examples of population density
problem for students to work on in groups and present solutions to the class are:
a. The YSU stadium has 20,630 seats. The dimension of sections 14-18 is 240 ft. by 160 ft. and
contains 3,630 seats. The distance from Petey’s white ball on his hat to the back edge of the
sections is 210 ft. Determine how many people a player can see if he is standing on the white
ball of Petey’s hat (see drawing below).
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TEACHING-LEARNING
TEACHER NOTES
(Solution: Area of large triangle: 25200 sq. ft., base of small triangle: 57 ft., area of small triangle:
1425, subtract the two areas to get area of the trapezoid (or use ½ h(b1 + b2 ), use proportion to find the
number of people: 2,247 people)
b. Schushsville is a triangular shaped island off the coast of Northville. Two sides of the island are
100 miles and 350 miles with a 24° between them. There are currently 250,000 inhabitants on
the island. Last year, there were 12,000 new children born and 10,000 people were recorded
as deceased. It is believed that the island could support a population as dense as 150
people/square mile. What is the current population density and what do you expect will happen
to the density as time goes on? Hint: to find the area, draw an altitude perpendicular to either
given side. (Ans: density is 35.4 people per sq. mi. and if this trend continues, the density
should increase gradually).
(G.MG.2, MP.1, MP.2, MP.4, MP.5, MP.6, MP.7, L.1, L.2)
17. An occupation for students who are geometrically inclined and creative, is engineering design,
creative design, and architecture. Below is a project for students to work on using design with
geometry: (G.MG.3, MP.2, MP.4, MP.5, L.2)
Select your favorite poem, song, or rap (school appropriate) and place it in an acute triangle whose
area is exactly half the page. Show your calculations for the areas on a post-it attached to the
paper. Materials needed: 8 ½ x 11 sheet of paper, ruler, protractor, calculator, and post-its.
At this time administer test #2 on standards G.MG.1, G.MG.2, and G.MG.3
6/30/2013
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TEACHING-LEARNING
18. Begin this section by deriving the formula for the area of a triangle: A = ½ *a * b * sin C. Before
TEACHER NOTES
this is begun, review the fact that opposite <A is side a, opposite <B is side b and opposite <C is
side c. Have students draw and label a triangle with a height starting at vertex B and perpendicular
to side b. Discuss the differences between A = ½ b*h and A = ½ *a * b * sin C. Pose the question:
“How can h = a sin C?”. Have prepared the proof written out in steps, copied and each step cut into
strips. Then have students put the steps in order working in small groups. Have them practice with
the other two versions: A = ½ *c * b * sin A and A = ½ *a * c * sin B and verbalize the location
between the two sides and the angle. (G.SRT.9, MP.1, MP.2, MP.3, MP.4, MP.7, MP.8, L.2, L.5)
(Proof: sin C = , multiply both sides by a to get a sin C = h, substitute a sin C for h into the area
formula A = ½ b*h.) Revisit example 16b in context of this formula.
19. Reinforce with the following problems: (G.SRT.9, MP.1, MP.4, MP.5, MP.6, MP.8, L.2)
a) ∆ABC, a = 15, b = 20 and <C = 35°, find the area (ans. 86)
b) In ∆ABC, a = 10, b = 30, and <C = 28°, find the area. (ans. 70.4)
c) In ∆ABC, a = 5, c = 8 and <C = 36, find the area (hint: draw altitude from B perpendicular to b)
(Ans. 16.75)
20. Place the law of sines on the board:
. Then have them take two of the 3
area formulas in section #18 and derive part of the law of sines. After they have completed that
part, have them choose another pair of area formulas and derive the remainder of the law of sines.
(G.SRT.10, MP.1, MP.2, MP.3, MP.4, MP.7, MP.8, L-2, L-5)
21. Reinforce the law of sines with the following: (G.SRT.10, G.SRT.11, MP.1, MP.4, MP.5, MP.6,
MP.8, L.2)
a) John wants to measure the height of a tree. He walks exactly 75 feet from the base of the tree
and looks up. The angle from the ground to the top of the tree is 33°. This particular tree grows
at an angle of 83° with respect to the ground rather than vertically (90°). How tall is the tree?
(Ans. 45.4)
b) A building is of unknown height. At a distance of 100 feet away from the building, an observer
notices that the angle of elevation to the top of the building is 41° and that the angle of
elevation to a poster on the side of the building is 21°. How far is the poster from the roof of the
building? (Ans 48.5 ft.)
c) A pilot is flying over a straight highway. He determines the angles of depression to two towers
(points B and C) 3.7 miles apart to be 67° and 59°. Find AB and determine the elevation of the
plane. (Ans: AB = 3.9 miles and elevation is 3.6 miles)
A
B
C
d) Problems arise when there is a possibility of an obtuse triangle. For instance, in triangle ABC,
<A = 25°, a = 8 and b = 11, find <B. Using the law of sines, there are two possible measures
for <B, 35° or 145°. Both angles have the same sine. So there are two solutions: if <B = 35,
then <C = 120 and AB = 16.4 and if <B = 145, then <C = 10, and AB = 3.3.
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TEACHING-LEARNING
TEACHER NOTES
22. To begin the discussion of the law of cosines, present this problem to the students: Three sides of
a triangular lot are 80 ft., 130 ft. and 170 ft. Find the measure of the angles at the corners of the lot.
Ask them how to solve this problem, discussing the possible use of the law of sines and the fact that
it cannot be used since no angles are known. This would give two unknowns in the law of sines. At
this time, discuss the need for a new law, the law of cosines, a2 = b2 + c2 – 2bc*cos A, b2 = a2 + c2 –
2ac*cos B, and c2 = a2 + b2 – 2ab*cos C. Then solve the lot problem using the law of cosines for
the first angle and then the law of sines for the last two angles. Note: when solving for the angles
knowing the three sides, always find the largest angle first. The reason for this is it might be obtuse
and using the law of sines would not show this because the sin x = sin (180-x) however the cosine x
= - cosine (180-x). Next discuss which law should be used for a problem where two sides and an
included angle are known and the unknown is the third side, such as the distance from a boat to two
points on the shore are 120 meters and 90 meters and the angle between them is 650. Find the
distance the two points are from each other. (Ans. 115.6 m) (G.SRT.11, MP.1, MP.2, MP.3, MP.4,
MP.5, MP.6, MP.8, L.2)
23. Reinforce with additional examples from the textbook in chapter 7 and also in the textbook web site:
http://www.glencoe.com/sec/math/geometry/geo/geo_04/ using the extra examples for section 7-7
and the self check quizzes for section 7-7. (G.SRT.11, MP.1, MP.4, MP.5, MP.6, MP.8, L.1, L.2)
Additional examples with answers
a) A lighting system for a restaurant is supported equally by two cables suspended from
the ceiling of the restaurant. The cables form a 150 angle with each other. If the lighting
system weighs 800 pounds, what is the force exerted by each of the cables on the
lighting system?
Draw a diagram of the situation. Then draw the vectors tip-to-tail.
Since the triangle is isosceles, the base angles are congruent. Thus, each base angle measures
180° - 30°
or 75. We can use the Law of Sines to find the force exerted by the cables.
2
800
x
=
sin 30° sin 75°
800 sin 75°
x = sin 30°
x = 1545.48
Law of Sines
The force exerted by each cable is about 1545 pounds.
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TEACHING-LEARNING
TEACHER NOTES
b) A lifeguard sits on lifeguard stand that is about eight feet high. He suddenly notices that
a swimmer is struggling in the water. The angle between the base of the lifeguard stand
and the swimmer is about 102°, and the straight line distance between the base of the
stand and the swimmer is about 85 feet. How far is the lifeguard from the swimmer?
In this problem, you know the
measurements of two sides of
a triangle and the included angle.
Use the Law of Cosines to find
the measure of the third side of
the triangle.
x2 = 82 + 852 - 2(8)(85) cos 102°
x2 = 7571.7599
x = 87.01586005
Use a calculator.
The lifeguard is about 87.0 feet from the swimmer.
c) Given: a = 15, b = 10, c = 22, solve the triangle
Recall that  and 180° -  have the same sine function value, but different cosine function values.
Therefore, a good strategy to use when all three sides are given is to use the Law of Cosines to
determine the measure of the possible obtuse angle first. Since c is the longest side, C is the angle
with the greatest measure, and therefore a possible obtuse angle.
c2
222
222 - 152 - 102
-2(15)(10)
2 - 152 - 102
22
cos-1 -2(15)(10) 
122.0054548
= a2 + b2 - 2ab cos C
= 152 + 102 - 2(15)(10) cos C
Law of Cosines
= cos C
=C
=C
Use a calculator.
So, C = 122.0°.
a
c
=
sin A sin C
15
22
=
sin A sin 122°
15 sin 122°
sin A =
22
15 sin 122°
A = sin-1 

22
A = 35.32506562
Law of Sines
Use a calculator.
So, A = 35.3°.
B = 180° - (122° + 35.3°)
B = 22.7°
6/30/2013
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TEACHING-LEARNING
TEACHER NOTES
The solution of this triangle is A = 35.3°, B = 22.7°, and C = 122°.
24. Derive the law of cosines with the students:
A
c
B
(a-x)
b
a
D x
C
Given: AD is perpendicular to BC and AD = h
c2 = (a-x)2 + h2
c2 = a2 – 2ax + x2 + h2
c2 = a2 – 2ax + b2, since x2 + h2 = b2
c2 = a2 – 2a(bcosC) + b2, since cosC = , x = b cosC
c2 = a2 + b2 – 2abcosC
There are several methods used to present this to students: write the steps on paper and cut each step
out and have students put steps in proper order or write the proof out and leave out steps or parts of
steps and have students fill in the blanks.
Have students then derive the other two forms of the law of cosines. (G.SRT.11, MP.2, MP.3, MP.4,
MP.5, MP.8, L.2)
Two web sites you might find helpful:
http://glencoe.mcgraw-hill.com/sites/dl/free/0078884845/634463/geosgi.pdf
(A study guide for geometry, extra problems, excellent site, 184 pages)
http://www.clarku.edu/~djoyce/trig/oblique.html
(Supplies additional problems for laws of sines and cosines.)
Have student take the third assessment for this unit involving standards G.SRT.9, G.SRT.10,
G.SRT.11)
TEACHER CLASSROOM ASSESSMENT
TEACHER NOTES
1. Quizzes
2. In class participation and practice problems for each concept
3. 2- and 4-point questions
TRADITIONAL ASSESSMENT
TEACHER NOTES
1. Paper-pencil test with M-C questions
AUTHENTIC ASSESSMENT
1. Give students a map of a section of Youngstown City with a scale. Instruct students to place three
cell phone towers on the map such that when they connect the towers with lines, a right triangle is
not formed. Label the triangle, then measure the sides using a ruler and angles using a protractor.
Using the scale, list the measurements on the drawing. Then find the area of the triangle, showing
your work. Make sure all measurements are labeled. (G.MG.3, G.SRT.9MP.1, MP.4, MP.5, MP.6,
L.2)
TEACHER NOTES
2. Students evaluate goals set at the beginning of the unit or on a weekly basis.
6/30/2013
YCS MATH GEOMETRY: UNIT 2B Trigonometry
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10
RUBRIC
ELEMENTS OF THE
PROJECT
Placed three cell phone
towers on the map
Labeled triangle
0
Did not attempt
Did not attempt
Scale measurements of
the sides
Did not attempt
Measurements of the
angles
Did not attempt
Area of triangle
Did not attempt
6/30/2013
1
Placed one tower
on the map
Labeled incorrectlydid not use capital
letters
Found scale
measurement of
one side correctly
Found
measurement of
one angle correctly
Errors in finding the
area
2
3
Placed two towers
on the map
NA
Placed three towers
on the map
Labeled correctly
using capital letters
Found scale
measurements of
two sides correctly
Found
measurements of
two angles correctly
Found the area
correctly, did not
show work or did
not label answer
Found scale
measurements of
three sides correctly
Found measurements
of three angles
correctly
Found area correctly,
showed work and
labeled answer
YCS MATH GEOMETRY: UNIT 2B Trigonometry
2013-2014
11
T-L #9: WORKSHEET #1: CLINOMETER PROJECT:
1. Build a clinometer using the two web sites: http://www.youtube.com/watch?v=CsNbfxDQnYM and
http://repository-intralibrary.leedsmet.ac.uk/open_virtual_file_path/i1442n87724t/shapestheod2_clinometer.pdf.
2. Choose 3 objects to find their heights such as a flagpole, basketball hoop, goal posts, building, etc.
3. Stand a certain distance away from the object and have someone measure this distance and record it.
4. Standing at the same spot, use your clinometers to measure the angle from you to the top of the object
and record it.
5. Repeat steps 3 and 4 with the other two objects.
6. Have someone measure your height.
7. On your paper draw your triangles and any other shapes representing the objects and you.
8. Label vertices and show your measurements.
9. Show your calculations for finding the height of the objects.
6/30/2013
YCS MATH GEOMETRY: UNIT 2B Trigonometry
2013-2014
12