Download Assignment sheet _ Special right Triangles and Trig

Date
Friday
01/20
GT/Honors Geometry
Jan 20 – February 9, 2017 – Special Right Triangles
Topic
Assignment
9-4 Similar Right triangles and Geometric mean.
Pg. 403: 4-10, 12a, 13-18, 26-29, 42-43
Complete WS in class
Monday
01/23
10-1 Simplifying radicals, Pythagorean triples, converse
of Pythagorean theorem.
Thuesday
01/24
10-1 Simplifying radicals, Pythagorean triples, converse
of Pythagorean theorem.
Complete Questions on WS
Pg. 427: 1-3, 6-12, 15-17, 30
Quiz 4 - Retention Quiz (Quadrilaterals unit)
Wednesday
01/25
Thursday
01/26
Friday
01/27
10-2 Special Rt. Triangles (day 1)
45-45-90 and 30-60-90 Triangles
10-2 Special Rt. Triangles (day 2)
45-45-90 and 30-60-90 Triangles
10-2 Special Rt. Triangles Applications.
Quiz 1: Special Right Triangles
Monday
01/30
Tuesday
01/31
Wednesday
02/01
Thursday
02/02
Friday
02/03
Special Rt. Triangles Applications.
Monday
02/06
Tuesday
02/07
Wednesday
02/08
Thursday
02/09
Friday
02/10
Pg. 433: 1-3, 6-18(odd) 21, 25, 27
WS A: 1-30 (evens)
WS B: 1-20 (evens)
Complete Review Questions
District Assessment (check point)
10-3 Trigonometric Ratios. Day 1:
SOH-CAH-TOA. WS C – in class.
10-3 Trigonometric Ratios. Day 2:
ARC SOH-CAH-TOA. Pg. 438: 1-25 in class
10-3 Trigonometric Ratios. Day 3:
ARC SOH-CAH-TOA. Pg. 438: 1-25 in class
Quiz 2: Similar and special Right Triangles (section
10.3).
10-4 Angles of Elevation & Depression
10-4 Applications of Trig – Day 2
Quiz 3: Similar and special Right Triangles.
(Section 10.4)
Review: Compare and contrast methods for solving
problems involving right triangles
Test 1: Special segments, Pythagorean, Special Right
Triangles
Proportional Relationships: (G.12B, G.12C, G.12D)
11.1 derive formulas using proportion for finding arc
length of a circle.
Progress Report #6 Ends
WS D: 1-24
WS E: 1-20 odds
WS E: 1-20 evens
WS F: 1-14, Pg. 443: 1-8 (odds), 9-13,
22, 26, 28
Complete Questions on WS,
pg 446:1-17, pg. 448: 1-20
1
Review- Pythagorean Theorem
2
3
4
5
Review Geometric mean: Find the geometric mean for each pair of numbers.
1) 7 and 9 ________ 2)
4)
8 2 and
14 and 14 _________
2 ________5) 10 and 8.1 ________
3)
2 3 and 3 _________
6)
9
25
_________
and
16
36
Use the figures to answer #1-7.
1) Find DB if AD = 4 and CD = 6.______
2) If AD = 2 and DB = 8, find CD.______
C
A
D
C
B
A
3) If AD = 3 and DB = 6, find AC.______
4) Find DB if BC = 6 and AD = 5.______
C
A
D
C
B
A
5) Find AD if DC = 4 and DB = 6.______
D
B
D
6) If AB = 12 and DB = 8, find AC.______
C
A
B
D
C
B
A
B
D
7)Find CD if AC = 3, BC = 4 and AB = 5.______
C
A
D
B
Find each indicated variable.
6
5
z
x
8) x = ______
y = ______
z = ______
9)
x = ______
y = ______
z = ______
y
4
10) x = ______
y = ______
z = ______
x
z
8
4 5
z
6
11) x = _______
y = _______
z = _______
x
z
y
12
x
18
y
20
x
12) x = ______
y = ______
z = ______
y
x
5
z
25
13) x = ________
y = ________
z = ________
12
z
y
16
14) A right triangle has an altitude of 8 m. and a leg length of 10 m. Find the length of its
hypotenuse and the length of the other leg.
hypot. = _______
leg = ________
15) A swimmer is sitting at a corner of an 80 ft. by 40 ft. pool. Stretched diagonally across
the pool opposite the swimmer is a string of plastic flags. How far must the swimmer swim
to reach the string of plastic flags?
Review- Simplifying Radicals
7
Simplify each of the following completely. Show all work neatly.
______1.
20
______2.
147
______3.
16
______4.
128
______5.
75
______6.
3 60
______7.
18
______8.
44
______9.
144
______10.
24
______11.
400
______12.
2 8
______13.
242
______14.
5 40
______15.
169
______16.
98
______17.
48
______18.
45
______19.
72
______20.
149
Multiply and simplify completely. Show all work neatly.
______21.
12 3  2
______22.
11 6  3
______23.
15 7  3
______24.
3 2
______25.
11 10  2
______26.
4 21  3
______27.
8 14  2
______28.
6 15  3
______29.
25 2  2
______30.
39 3  3
______31.
84 5  2
______32.
7 2 3
______33.
41 22  2
______34.
13 7  3
Perform the indicated divisions and rationalize all denominators. Show all work neatly.
8
______35.
12
3
______50
15
2
______36.
11
2
______51.
47 30
2
______37.
14 2
3
______52.
8 5
2
______38.
18 5
3
______53.
15 8
3
______54.
8 2 8 3 5 3 2 2
______55.
7 5 8 5
______39.
3
3
______40.
26 15
3
______41.
7 3
2 2
______42.
12 6
2
______43.
3 3 5 3
______44.
8 2 3 2 5 3
______45.
9 3 6 3
______46.
______47.
8
2
17
3
______48.
11 3
2
______49.
12 7
2
9
Geometry
Worksheet 8.2 A – Special Right Triangles
Name ________________________
Date _____________ Period ____
Given the following 45º - 45º - 90º and 30º - 60º - 90º triangles, find the length of each missing side.
1. x = ______
2. x = ______
x
y = ______
y
y = ______
45
3 º
y
45
x º
6
x
3. x = ______
4. x = ______
x
y = ______
y
45
º
y = ______
20
y
26
6. x = ______
y
x
y = ______
45
º
4 2
5. x = ______
45
º
x
y = ______
45
º
1
2
y
7. x = ______
y = ______
x
8. x = ______
x
45
º
y
45
º
y = ______
45
º
3 14
5
9. x = ______
y = ______
y
10. x = ______
x
45
º
x
y
9
y
y = ______
45
º
11. x = ______
45
º
12
12. x = ______
x
y = ______
y
4
45
º
x
y = ______
45
º
y
5 2
10
Given the following 30º - 60º - 90º triangles, find the length of each missing side.
13. x = ______
14. x = ______
60
º 3
x
y = ______
30
º
y = ______
x
60
º
y
6 3
y
15. x = ______
x
16. x = ______
x
y
y = ______
60
º
30
º
30
º
y = ______
30
º
8
y
60
º
20
17. x = ______
18. x = ______
y
x
y = ______
y = ______
60
º
30
º
x
y
17
1
2
19. x = ______
20. x = ______
x
y = ______
60
º y
30
º
x
30
º
y = ______
y = ______
x
22. x = ______
60
º
60
º
24
5 6
21. x = ______
y
y
2 5
y
y = ______
30
º
x
9
23. x = ______
24. x = ______
x
y = ______
y
30
º
5 3
y = ______
x
30
º
60
º 7 6
11
y
9
25. Given the isosceles trapezoid, find x.
14
45
x
26. Find the perimeter of the isosceles trapezoid.
24
60
32
27. The altitude BD to the base AC of isosceles ABC has a length of 12. If AC = 10,
find the perimeter of ABC.
28. Find the perimeter of a rectangle with diagonal 17 and width 8.
29. A man travels 7 miles due north, 2 miles due east, 3 miles due south and 1 mile due
east. How far is he from the starting point?
30. The perimeter of an equilateral triangle is 36. Find the length of an altitude.
12
8.2 B WORKSHEET ON RIGHT TRIANGLES
1. Find the length of each altitude.
a. _______ b. ________ c. ________
12
12
60
12
45
60
30
45
30
2. Find x, y, k, and m.
x=________
y=________
k=________
m=________
x
6
y
45
30
m
k
______3. Find the length of a side of a square
whose diagonal measures 20.
______4. Find the length of a side of an
equilateral triangle whose altitude measures 27.
______5. An isosceles triangle has base angles
30˚ and base measure 12. Find the length of the
altitude to the base.
R
6. MR = 6
MP = ______
PR = ______
PQ = ______
135
Q
7. BC = 8 3
AC = ______
AB = ______
CD = ______
A
M
P
________8. Find the perimeter of this isosceles
10
trapezoid.
D
30
C
B
x
_________9. Find x.
30
60
16
_________10. Find x.
x
15
8.5
15
12
12
3
35
13
13
11. If JG is the altitude to the base FH of
isosceles triangle JFH, FJ = 15, and FH = 24,
find JG.
13. Nadia skips 3 m. north, 2 m. east, 4 m. north, 13
m. east, and 1 m. north. How far is Nadia from
where she started?
12. PM is an altitude of equilateral triangle PKO.
If PK = 4, find PM.
14. Find CD in trapezoid ABCD with bases AD and
BC . Find the perimeter of this trapezoid.
A
30
D
8
B
10
C
15. A rectangle 6 in. wide has a diagonal 10 in. long.
Find the perimeter.
16. A man travels 7 mi. due north, 6 mi. due east,
and then 4 mi. due north. Ho far is he from his
starting point?
17. A man travels 7 mi. due north, 3 mi. due east,
and then 3 mi. due south. How far is he from his
starting point?
18. The legs of an isosceles triangle are 6 in. long.
If the base is 8 in. long, find the length of the
altitude to the base.
19. Find the length of an altitude of an equilateral
20. An isosceles right triangle has a 6 in.
hypotenuse. Find the length of a leg.
triangle with a side 2 3 in. long.
14
Name____________________________________
Introduction to Trigonometry Notes
“SOHCAHTOA”
Today we are going to start looking at trigonometric, or “trig” functions. There are buttons for each of these
functions on your calculator and you have probably noticed them before. Sin, Cos, and Tan are the buttons on your
calculator that stand for Sine, Cosine, and Tangent.
Each of the functions represents a fraction that you can write using the sides of the triangle.
Before you can write the fraction, you need to figure out which sides of the triangle you need to
use. This brings us to what SOHCAHTOA stands for:
Sin Opposite Hypotenuse Cos Adjacent Hypotenuse Tan Opposite Adjacent
So how do we use this? SOHCAHTOA tells you which sides to use in relation to the angle you are looking at. There
are a few steps to doing these problems.
1.
2.
3.
4.
5.
Mark the angle you are looking at.
Label the sides in relation to the angle you are looking at. (opposite, adjacent, hypotenuse)
Circle the sides you are supposed to use to make that trig function (use SOHCAHTOA) to help you.
Decide which side goes on top of the fraction (numerator) and which goes on bottom of the fraction
(denominator).
Write the fraction.
Here are a few examples:
EX 1 Find sin A.
B
13
5
C
A
12
1.
2.
3.
4.
5.
Mark angle A.
Label the sides in relation to angle A (opp, adj, hyp)
Circle the sides that we use for sin (opp, hyp)
Decide which side goes on top of the fraction (opp)
Write the fraction.
Sin A = _________
EX 2 Find cos B
B
1.
2.
3.
4.
5.
13
5
C
12
A
EX 3 Find tan A
B
5
C
12
Cos B = _________
1.
2.
3.
4.
5.
13
A
Mark angle B.
Label the sides in relation to angle B (opp, adj, hyp)
Circle the sides that we use for cos (adj, hyp)
Decide which side goes on top of the fraction (adj)
Write the fraction.
Mark angle A.
Label the sides in relation to angle A (opp, adj, hyp)
Circle the sides that we use for tan (opp, adj)
Decide which side goes on top of the fraction (opp)
Write the fraction.
Tan A = _________
15
Name______________________________
Trigonometry with the Calculator
You have learned what sin, cos, and tan mean. Each is a fraction you can write using the sides of
a right triangle. But what if you don’t know one of those sides? That is where the calculator
can help you.
We are still going to use SOHCAHTOA to help us. But we need to practice using the calculator
before we get to working any problems.
First you need to check that your calculator is in the right mode. It should be in degrees mode.
Try entering Sin 30°. If you get 0.5 you are in the right mode. Otherwise you need to change
it.
After you are sure that you are in degrees mode we are ready to start. Your calculator has
information stored into it for every possible angle measure. Enter each of these into your
calculator:
1. cos 45° ________
2. sin 36° ________
3. tan 18° ________
4. sin 18°
We could keep entering values all day and your calculator would know the answer. (But don’t
worry, we won’t)
Now we will do a couple of examples of how to use the calculator to solve for a missing side.
Here are the steps you need to use:
1. Mark the angle that you are going to use for this problem (usually the one that you are given
– careful, don’t use the right angle!)
2. Label the sides in relation to the angle that you are going to use (opposite, adjacent,
hypotenuse)
3. Circle the sides you are going to use to make a trig function.
4. Decide which trig function you can make with those sides, either sin, cos, or tan.
5. Write the equation, using a variable for the missing side.
6. Solve the equation for the missing side. (using algebra steps)
Here are a few examples:
EX 1 Find x.
B
x
C
13
34
°
A
1.
2.
3.
4.
5.
6.
Mark angle A (since it is the one that we have a measure for)
Label the other two sides in relation to angle A (opp, hyp)
Circle these sides.
Decide which trig function you can make with Opp, Hyp (sin)
Write the equation, using the variable x for the missing side.
Solve the equation for x, using algebra.
16
EX 2 Find x.
B
67
x °
18
A
C
1.
2.
3.
4.
5.
6.
Mark angle B (since it is the one that we have a measure for)
Label the other two sides in relation to angle B (adj, hyp)
1.
Mark angle A (since it is the one that we have a measure for)
Label the other two sides in relation to angle A (opp, adj)
Circle these sides.
Decide which trig function you can make with Opp, Adj (tan)
Write the equation, using the varialbe x for the missing side.
Solve the equaiton for x, using algebra.
Circle these sides.
Decide which trig function you can make with Adj, Hyp (cos)
Write the equation, using the variable x for the missing side.
Solve the equation for x, using algebra.
EX 3 Find x.
B
x
C
43
°
9
A
2.
3.
4.
5.
6.
EX 4 Find x. (this one is a little different!)
B
20
C
x
52
°
A
1.
2.
3.
4.
5.
Mark angle A (since it is the one we have a measure for)
Label the other two sides in relation to angle A (opp, hyp)
Circle these sides.
Decide which trig function you can make with Opp, Hyp (sin)
Write the equation, using the variable x for the missing side.
Be careful here, this is different than the others. Where does
x go?
6. Solve the equation for x, using algebra.
17
Name_____________________How to find a Missing Angle using Trig
So far we have just used trig to find missing measures of sides. We can also use it to find
missing angles when we know two of the sides. You are going to use your calculator a little
differently to do this.
When we know the sides, but don’t use the angle we have to tell our calculator that we want to
know an angle measure. The way we do this is by pressing 2nd, then either sin, cos, or tan. Then
the calculator tells us the degree measure. Here is how it works: (round to the nearest degree)
1. sin A = 0.4226
A = _______
2. cos B = 0.6691
B = ________
3. tan R = 0.2679
R = _______
4. sin Z = 0.8290
Z = ________
There are steps we need to use when we are looking for the missing angle measure in a problem.
1. Mark the angle that you are looking for.
2. Label the given sides in relation to the angle that you need to find.
3. Decide which trig function (sin, cos, or tan) you can write with the sides that you have been
given.
4. Write out the trig function.
5. Use the 2nd sin, cos, or tan to tell you the missing angle.
Here are a few examples.
EX 1 Find the missing angle, “x”
14
5
x
1.
2.
3.
4.
5.
Mark the angle that we are looking for, x.
Label the given sides in relation to x. (opp, hyp)
Decide which trig function goes with Opp, Hyp (sin)
Write out the trig function.
Use your calculator to tell you the degree measure.
EX 2 Find the missing angle, “x”
5
x
14
1.
2.
3.
4.
5.
Mark the angle that we are looking for, x.
Label the given sides in relation to x. (opp, adj)
Decide which trig function goes with Opp, Adj (tan)
Write out the trig function.
Use your calculator to tell you the degree measure.
18
Trigonometry Homework
WS C: Writing Trigonometric Ratios
1.
2.
A
5
9
13
C
12
3.
41
B
sin A = ______
B
4.
A
5
3
C
C
A
40
sin A = ______
B
17
8
C
B
4
cos B = ______
5.
A
15
cos A = ______
6.
25
B
7
C
24
7.
B
S
A
8
C
9.
A
15
C
50
14
H
tan A = ______
40
cos S = ______
G
39
C
11.
R
12
10.
36
B
15
T
sin A = ______
tan R = ______
S
9
10
T
24
tan A = ______
8.
6
R
10
26
A
F
48
cos F = ______
12.
B
Y
75
9
41
A
X
72
sin A = ______
13.
21
Z
tan Y = ______
14.
J
10
K
G
26
17
8
H
M
cos H = ______
24
15.
16.
B
34
A
30
S
16
C
4
sin A = ______
T
H
15
4
cos G = ______
R
4 2
tan R = ______
19
Trigonometry Homework
WS D: Finding Missing Sides
1.
2.
32
49
x
28
34
x
x= ______
3.
x= ______
4.
19
35
x
24
42
x
x = ______
5.
x = ______
6.
53
36
41
x
27
x
x = ______
7.
x = ______
8.
48
72
9
x
19
x
x = ______
9.
x
32
Careful!
x= ______
10.
23
x
39
x = ______
11.
21
x= ______
12.
17
36
x
x
27
x = ______
78
x= ______
20
13.
Be careful! These
problems are different!
x
14.
24
24
24
24
x
x = ______
15.
x = ______
16.
39
x
x
43
65
27
x = ______
17.
x = ______
18.
68
x
99
x
38
37
x = ______
19.
x = ______
20.
7
x
x
45
12
30
x = ______
21.
x = ______
22.
45
x
33
x
75
8 2
x = ______
23.
x = ______
24.
x
46
34
x
40
x = ______
88
x = ______
21
Geometry
Name__________________________________
Worksheet E – Trig Ratios in Right Triangles Name_____________________Period_______
For each of the following, write the equation to find the missing value. Then rewrite the equation that
you will enter in your calculator. Round your final answer to the nearest tenth.
1.
2.
x  _______
x  _______
8
y
y  _______
y  _______
x
8
36
y
x
4
3.
x  _______
y  _______
4.
x  _______
y  _______
x
10
x
64
y
5
5.
x  _______
y  _______
y
50
6.
x  _______
y  _______
12
x
y
x
70
4
y
7.
x  _______
y  _______
m  B=______
B
20
y
16
A
9.
w  _______
x  _______
y  _______
z  _______
7.2
40˚
z
w
x
11. How tall is the tree?
25˚
y
C
9
x
37
A
C
x
20
8.
x  _______
y  _______
m  A=_______
10.
h  _______
x  _______
y  _______
h
y
B
x
10
110 55˚
˚
y
12. A man who is 6 feet tall is flying a kite. The
kite string is 75 feet long. If the angle that the
kite string makes with the line horizontal to the
ground is 35, how far above the ground is the kite?
62
31’
22
13. A ladder 14 feet long rests against the side of a building. The base of the ladder rests on level ground
2 feet from the side of the building. What angle does the ladder form with the ground?
14. A 24-foot ladder leaning against a building forms an 18˚ angle with the side of the building. How far is
the base of the ladder from the base of the building?
15. A road rises 10 feet for every 400 feet along the pavement (not the horizontal). What is the
measurement of the angle the road forms with the horizontal?
16. A 32-foot ladder leaning against a building touches the side of the building 26 feet above the ground.
What is the measurement of the angle formed by the ladder and the ground?
17. The directions for the use of a ladder recommend that for maximum safety, the ladder should be
placed against a wall at a 75˚ angle with the ground. If the ladder is 14 feet long, how far from the
wall should the base of the ladder be placed?
18. A kite is held by a taut string pegged to the ground. The string is 40 feet long and makes a 33˚ angle
with the ground. Supposing that the ground is level, find the vertical distance from the ground to the
kite.
19. A wire anchored to the ground braces a 17-foot pole. The wire is 20 feet long and is attached to the
pole 2 feet from the top of the pole. What angle does the wire make with the ground?
20. A jet airplane begins a steady climb of 15˚ and flies for two ground miles. What was its change in
altitude?
23
Geometry Worksheet F
8.5 (Angles of Elevation & Depression)
Name__________________________________
Date___________________Period__________
Draw a picture, write a trig ratio equation, rewrite the equation so that it is calculator ready and then
solve each problem. Round measures of segments to the nearest tenth and measures of angles to the
nearest degree.
________1. A 20-foot ladder leans against a wall
so that the base of the ladder is 8 feet from the
base of the building. What is the ladder’s angle of
elevation?
________2. A 50-meter vertical tower is braced
with a cable secured at the top of the tower and tied
30 meters from the base. What is the angle of
depression from the top of the tower to the point on
the ground where the cable is tied?
________3. At a point on the ground 50 feet from
the foot of a tree, the angle of elevation to the top
of the tree is 53. Find the height of the tree.
________4. From the top of a lighthouse 210 feet
high, the angle of depression of a boat is 27. Find
the distance from the boat to the foot of the
lighthouse. The lighthouse was built at sea level.
________5. Richard is flying a kite. The kite
string has an angle of elevation of 57. If Richard
is standing 100 feet from the point on the ground
directly below the kite, find the length of the kite
string.
________6. An airplane rises vertically 1000 feet
over a horizontal distance of 5280 feet. What is the
angle of elevation of the airplane’s path?
________7. A person at one end of a 230-foot
bridge spots the river’s edge directly below the
opposite end of the bridge and finds the angle of
depression to be 57. How far below the bridge is
the river?
________8. The angle of elevation from a car to a
tower is 32. The tower is 150 ft. tall. How far is
the car from the tower?
230
24
________9. A radio tower 200 ft. high casts a
shadow 75 ft. long. What is the angle of elevation
of the sun?
________10. An escalator from the ground floor to
the second floor of a department store is 110 ft long
and rises 32 ft. vertically. What is the escalator’s
angle of elevation?
110
32
________11. A rescue team 1000 ft. away from
the base of a vertical cliff measures the angle of
elevation to the top of the cliff to be 70. A
climber is stranded on a ledge. The angle of
elevation from the rescue team to the ledge is 55.
How far is the stranded climber from the top of the
cliff? (Hint: Find y and w using trig ratios. Then
subtract w from y to find x)
________12. A ladder on a fire truck has its base 8
ft. above the ground. The maximum length of the
ladder is 100 ft. If the ladder’s greatest angle of
elevation possible is 70, what is the highest above
the ground that it can reach?
100
x
y
8
w
1000
________13. A person in an apartment building
sights the top and bottom of an office building 500
ft. away. The angle of elevation for the top of the
office building is 23 and the angle of depression
for the base of the building is 50. How tall is the
office building?
________14. Electronic instruments on a treasurehunting ship detect a large object on the sea floor.
The angle of depression is 29, and the instruments
indicate that the direct-line distance between the
ship and the object is about 1400 ft. About how far
below the surface of the water is the object, and how
far must the ship travel to be directly over it?
1400
500
25
TEST REVIEW
PYTHAGOREAN THEOREM, SPECIAL RIGHT TRIANGLES, TRIG. RATIOS
1. At a point on the ground 100 ft. from the foot of a flagpole, the angle of elevation of the top of the
pole contains a 31 degree angle. Find the height of the flagpole to the nearest foot.
2. Find the length of the side of a square whose diagonal is 6.
3. From the top of a lighthouse 190 ft. high, the angle of depression of a boat out at sea is 34 degrees.
Find to the nearest foot, the distance from the boat to the foot of the lighthouse.
4. The congruent sides of an isosceles triangle are each 15 in. and the base is 24 in. Find the length of
the altitude drawn to the base.
5. If cos A = sin 30, then angle A measures how many degrees?
6. Find the length of the diagonal of a square whose side is 6 in. in length.
7. Find to the nearest degree the measure of the angle of elevation of the sun if a post 5 ft. high casts a
shadow 10 ft. long.
8. The lengths of the bases of an isosceles trapezoid are 8 and 14 and each of the bases angles
measures 45 degrees. Find the length of the altitude of the trapezoid and the length of the legs.
9. In triangle ABC, angle C is a right angle, AC = 5, BC = 12.
a) Find AB.
b) Find the tan B.
c) Find sin B.
d) Find cos B.
e) Find the measure of angle B to the nearest degree.
C
10. AO = ________
B
2
A
AB = ________
OB = ________
OC = ________
OD = ________
D
45
60
30
O
CD = ________
DE = ________
OE = ________
60
E
11. How many feet of walking would a person save by cutting across the
vacant lot instead of taking the sidewalk around the outside edge?
X
120
160
12. How many inches long must each side of a cubical box be if the
distance from one corner is 12 in.? Answer with an expression in
simplest form.
Y
12
26
13. At a time of day when the sun can be sighted at an angle of 60 above the horizon, a flagpole casts
a shadow that is 21 ft long. How tall is the flagpole?
14. The perimeter of a square is 72. What is the length of the diagonal of the square?
15. Find the length of the altitude of an equilateral triangle with perimeter 48.
16. A rectangular box has a square base the area of which is 64 cm2. The height of the box is 12 cm.
Find the length of the interior diagonal of the box.
17. Find the slant height of a regular square pyramid if the altitude is 12 and one of the sides of the
square base is 10.
18. A decorator wants the sides of a rectangular picture frame to be in the ratio 7 to 24. If the diagonal
is 100 cm. long, what should the lengths of the sides be?
19. A flagpole is at the top of a building. Four hundred feet from the base of the building, the angle of
elevation to the top of the pole is 22°, and the angle of elevation to the bottom of the pole is 20°.
Sketch a figure. To the nearest foot, find the length of the flagpole.
20. The dimensions of a rectangular solid are in the ratio 3:4:5. If the interior diagonal is 200 2 , find
the three dimensions.
21. Terry drove 5 miles east, 7 miles north, 6 miles east, 2 miles south, and 1 mile east. How far is he
from his starting point?
Answers:
1. 60 feet
2.
3 2
3.
282 feet
4.
9 inches
5.
60°
6.
6 2
7.
27°
8.
altitude = 3; leg =
9.
(a) 13; (b) 5/12; (c) 5/13; (d) 12/13; (e) 23°
10. AO =
inches
3 2
3 ; AB = 1; OB = 2; OC = 2 2 ; OD = 4 2 ; CD = 2 6 ; DE =
8 6
4 6
; OE =
3
3
11. 80 feet
12.
4 3 inches
13.
21 3 feet
14.
18 2
15.
8 3
16.
4 17 cm.
17. slant height = 13
18. 28 cm and 96 cm
19. 16.022 or about 16 feet
20. 120, 160, and 200
21.
13 miles.
27