Download M60 Sec 4.6: Dimensional Analysis

M60 Sec. 4.4 Triangles
Part A: Angles and Triangles:
Angle:
Ex. 1: Label the sides and vertex of the angle:
Triangle:
Ex. 2: Label and name the triangle:
Ex. 3: Use a protractor to measure the angles in the triangle: You will need a protractor to do
your homework.
Acute angle:
Right angle:
M60 Sec. 4.4 p.2
Obtuse angle:
Straight angle:
One complete revolution:_____________
The sum of all three angles in any triangle is ______________.
Ex. 4: Use a protractor to draw a triangle with two angles that measure 46° and 59°. Label the third
vertex C.
A
B
Measure angle C.__________. Do the sum of all three angles equal 180°? (Or close to it?)
M60 Sec. 4.4 p.3
Part B: Similar Triangles:
Similar Triangles have the same __________________ and the same ____________
measurements.
50⁰
90⁰
50⁰
40⁰
90⁰
40⁰
Label the angles.
Name the corresponding angles:
Mark the corresponding sides:
Name the corresponding sides:
Use the correct notation to show that these two triangles are similar: Order is important!
Name them in another way:
R
Ex. 5: ∆ ABC and ∆ PQR are similar triangles:
A
P
Q
B
C
Mark the corresponding angles:
List the corresponding angles: A and P,
Mark the corresponding sides:
List the corresponding sides: AB and PQ,
Name each triangle another way that correctly relates the corresponding sides and angles:
M60 Sec. 4.4 p.4
Part C: Equations and Triangles:
Remember that the sum of all three angles must be ___________
Ex. 6: In
In  XYZ, angle Y is 13° more than angle Z, and angle X is 20° more than angle Z. Write an equation and
find the measures of all three angles of  XYZ.
Ex. 7: In  DEF, angle E is 15° less than angle D, and angle F is 21° less than angle D. Write an equation
and find the measures of all three angles of  DEF.
M60 Sec. 4.5: Ratios and Proportions:
Part A: Ratios:
Ratios:
Ex. 1: In the year 2010-2011 the faculty and staff numbers for LBCC were as follows:
Total Faculty: 532
Total Classified Staff: 514
Full-Time Faculty: 162
Full-Time Classified: 225
Part-Time Faculty: 369
Part-Time Classified: 289
What is the ratio of full-time faculty to part-time faculty? Simplify your answer.
Explain in words what the ratio means.
What is the ratio of full-time classified to total classified staff?
Part B: Proportions:
Proportion:
Cross Products and Proportions
Sec. 4.5 p.2
Part C: Solving Proportions:
Ex. 2: Solve each of the following proportions:
Part D: Applying Proportions:
First, you must make sure the things being compared are proportional. Either it has to be
stated, or you have to know they compare proportionally.
Ex. 3: Kathy's car gets 48 miles per gallon. How many gallons of gas will she need for a 2700mile road trip?
Ex. 4: A farm has an average yield of 48 bushels of soy beans per acre. The farm needs to
produce 4500 bushels of soybeans, how many acres should be planted?
Ex. 5: Nancy is planning a week-long bicycling trip, using a map with a scale of 1 inch equivalent
to 5 miles. On the map, the distance from her current location to the next town is about 6
inches. How far is Nancy from the next town?
Sec. 4.5 p.3
Ex. 6: Sue is making her favorite brownie recipe. The recipe calls for C of butter and 1
C of sugar. She only has C of butter. How much sugar does she need to use?
Ex. 7: An ODFW wants to estimate the number of deer in a certain forest using the mark-andcapture method. He catches 15 deer and tags them with and ear tag and then returns them to
the forest. The following week, he returns and captures 12 deer and finds 5 of those tagged.
Based on this sample, how many deer are there in that forest?
Part E: Similar Triangles Revisited: An important property to help solve for missing sides
of similar triangles.
Sides of Similar Triangles are ________________________. If two triangles are ____________,
Their corresponding sides have the same _______________.
Ex 8:  ABC

 DEF Corresponding angles are marked with the same sign. Find the missing sides.
D
A
56
x
y
6
C
45
B
F
E
9
Sec. 4.5 p.4
Ex 9:  ABC

 PQR Find the missing sides:
B
R
t
x
2
Q
2
C
A
Ex 10:  ABC

2.6
P
3
 XYZ Find the missing sides:
k
X
B
3.6
Y
n
5.4
A
5.7
C
3.2
Z
Ex. 11: Determine if the triangles are similar
4
7
5
5
6
2
3
M60 Sec 4.6: Dimensional Analysis - Basic Conversions
Review:
Multiplication and Division of fractions:
Part A: Unit Fractions:
Look at the Conversion Chart: Appendix B
1 yd = 3 ft
creates two _________ _____________
___________
OR
_____________
With dimensional analysis, we choose the fraction that _________ the units we
want to get rid of and ______________ the units we want to end up with.
Process of Dimensional Analysis or Unit Analysis:
1.
Write what you have as a ________________
2.
Look at where you want to _______ ____ (leave some room).
3.
Choose the unit fraction(s) from the conversion chart that
cancels the units you want to _____ ____ ___ and leaves
the units you want to _______.
Sec. 4.6 pg.2
Part B: Use dimensional analysis to convert units:
Ex. 1. 3 lbs = _____oz
Ex. 2: 15m = _____ ft
Ex. 3: 150 gal = _____ft³
Ex. 4: 15 acres = _____ ft²
Part C: Extending the Process:
Sometimes you will need to multiply by several unit fractions (chaining).
Ex. 5: 3400 kg = _____ oz
Sec. 4.6 pg.3
Ex. 6: 0.25 mi = _____ m
Ex. 7: Convert 30 yards into inches.
Ex. 8: The dimensions of a soccer field are 110m by 70m. What are the dimensions
rounded to the nearest yard?
Ex. 9: The average American eats 1483 pounds of candy in a lifetime.
a. How many ounces is this?
b. Suppose that a typical candy bar weighs 3.2 oz. The average American
eats the equivalent of how many candy bars in his/her lifetime?
Sec. 4.6 pg.4
Ex. 10: Stefanie just turned 23 years old, how many minutes old is she?
Ex. 11: The shark tank at the local aquarium is 385,000 gallons. How many liters is
this?
Ex. 12: How many 8 oz. servings of coffee can be gotten from a 1 Liter coffee pot?
Ex. 13: Esther’s living room is 12ft by 15 ft. The new carpet she wants costs $22.50
per square yard. How much will it cost to have the room carpeted?
M60 Section 4.7: Dimensional Analysis - Area and Volume
Area is measured in ___________________ units. Ex:
Volume is measured in _______________ units. Ex:
Part A: Converting Units of Area
1 square foot:
1 square yard:
Note: When converting area in units² the exponent of 2 on the units is a reminder that there are
________ dimensions to consider. You must use the unit fraction ___________.
Use Dimensional Analysis to perform the following conversions:
Ex. 1:
420
= _____
Ex. 2:
16 in² = _____ cm²
Ex. 3:
75
= _____
Sec. 4.7 pg.2
Ex. 4:
25,000 m² = _____mi²
Ex. 5:
1,000,000 mm² = _____ m²
Ex. 6:
64,000 ft² = _____ acres
Part B: Converting Units of Volume:
1 cubic foot:
1 cubic meter:
Note: When converting volume in units³, the exponent 3 is a reminder that there are ___________
dimensions to consider. You must use the unit fraction ____________times.
Ex. 7:
0.009 m³ = _____ in³
Sec. 4.7 pg.3
Ex. 8:
6 yd³ = _____ ft³
Ex. 9:
12,000,000 yd³ = _____ km³
Ex. 10: 0.085 km³ = _____ cm³
Ex. 11: The cranial capacity of a human is around 1500 cm³. What is this volume in in³ ?
Sec. 4.7 pg.4
Ex. 12: A fish tank measure 25 inches by 16 inches by 12 inches. How many cubic feet of water will it
hold? How many gallons is that?
Ex. 13: A raised bed for vegetable gardening is enclosed by a wooden frame that measures 4 ft by 9 ft
by 2 ft. How many cubic feet of soil will it take to fill the bed? How many cubic yards? If necessary,
round to two decimal places.
Ex. 14: A room measures 16 ft by 14 ft. Find the area of the room in square feet. Use dimensional
analysis to convert the area into square yards. What would it cost of carpet the room if the carpet sells
for $21.99 per square yard? Round your answer to the nearest cent.