Unit 2 - Review for Midterm Exam
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Determine tan A and tan C.
C
4
A
6
B
A) tan A = 1.5; tan C = 0.6
B) tan A = 0.6; tan C = 0.8321...
____
C) tan A = 0.6; tan C = 1.5
D) tan A = 0.5547...; tan C = 1.5
2. Determine the measure of D to the nearest tenth of a degree.
13
D
E
7
F
A) 28.3°
____
B) 32.6°
C) 57.4°
D) 61.7°
3. Determine the angle of inclination of the line to the nearest tenth of a degree.
|
4.1
|
9.7
A) 65.0°
B) 22.9°
C) 67.1°
D) 25.0°
____
4. Calculate the angle of inclination, to the nearest tenth of a degree, of a road with a grade of 19%.
A) 79.0°
B) 79.2°
C) 10.8°
D) 11.0°
____
5. A ladder leans against the side of a building. The top of the ladder is 4.5 m from the ground. The base of the
ladder is 1.0 m from the wall. What angle, to the nearest degree, does the ladder make with the ground?
A) 77°
B) 13°
C) 10°
D) 82°
____
6. Determine the tangent ratio for K.
L
M
20
101
K
A) 20
99
____
B)
20
101
C) 101
20
D) 99
20
7. Determine the length of side z to the nearest tenth of a centimetre.
X
3.8 cm
z
65°
Z
Y
A) 9.0 cm
____
B) 1.8 cm
C) 4.2 cm
D) 8.1 cm
8. Determine the length of side l to the nearest tenth of a metre.
L
16.1 m
M
l
57°
N
A) 10.5 m
____
B) 24.8 m
C) 13.5 m
D) 8.8 m
9. A guy wire is attached to a tower at a point that is 5.5 m above the ground. The angle between the wire and
the level ground is 56. How far from the base of the tower is the wire anchored to the ground, to the nearest
tenth of a metre?
A) 3.1 m
B) 6.6 m
C) 3.7 m
D) 8.2 m
____ 10. A ladder leans against a wall. The base of the ladder is on level ground 1.2 m from the wall. The angle
between the ladder and the ground is 70. How far up the wall does the ladder reach, to the nearest tenth of a
metre?
A) 0.4 m
B) 1.3 m
C) 3.5 m
D) 3.3 m
____ 11. A road has an angle of inclination of 16. Determine the increase in altitude of the road, to the nearest metre,
for every 175 m of horizontal distance.
A) 610 m
B) 168 m
C) 50 m
D) 48 m
____ 12. A flagpole casts a shadow that is 21 m long when the angle between the sun’s rays and the ground is 48.
Determine the height of the flagpole, to the nearest metre.
A) 19 m
B) 16 m
C) 14 m
D) 23 m
____ 13. A surveyor held a clinometer 1.5 m above the ground from a point 60.0 m from the base of a tower. The angle
between the horizontal and the line of sight to the top of the tower was 21. Determine the height of the tower
to the nearest tenth of a metre.
A) 157.8 m
B) 23.0 m
C) 24.5 m
D) 65.8 m
____ 14. From a point 18 ft. from the base of a flagpole, Seema used a clinometer to sight the top of the flagpole.
Seema held the clinometer 5 ft. 3 in. above the ground. The angle between the horizontal and the line of sight
was 52. Determine the height of the flagpole to the nearest foot.
A) 28 ft.
B) 34 ft.
C) 19 ft.
D) 23 ft.
____ 15. Determine sin G and cos G to the nearest hundredth.
40
F
E
9
41
G
A) sin G = 0.98; cos G = 4.56
B) sin G = 0.22; cos G = 0.98
C) sin G = 1.03; cos G = 0.22
D) sin G = 0.98; cos G = 0.22
____ 16. Determine the measure of D to the nearest tenth of a degree.
D
E
10
23
F
A) 64.2°
B) 66.5°
C) 25.8°
____ 17. Determine the measure of Q to the nearest tenth of a degree.
D) 23.5°
P
13
Q
25
R
A) 58.7°
B) 62.5°
C) 31.3°
D) 27.5°
____ 18. A helicopter is hovering 350 m above a road. A car stopped on the side of the road is 450 m from the
helicopter. What is the angle of elevation of the helicopter measured from the car, to the nearest degree?
A) 52°
B) 39°
C) 51°
D) 38°
____ 19. A ladder is 11.0 m long. It leans against a wall. The base of the ladder is 3.3 m from the wall. What is the
angle of inclination of the ladder to the nearest tenth of a degree?
A) 72.5
B) 17.5
C) 73.3
D) 16.7
____ 20. Determine the length of MN to the nearest tenth of an centimetre.
L
M
15.8 cm
51°
N
A) 19.5 cm
B) 25.1 cm
C) 9.9 cm
D) 12.3 cm
____ 21. Determine the length of XY to the nearest tenth of a centimetre.
Y
X
20.1 cm
59°
Z
A) 10.4 cm
B) 17.2 cm
C) 33.5 cm
____ 22. Determine the length of RS to the nearest tenth of a metre.
D) 23.4 cm
R
29°
18.8 m
T
A) 21.5 m
S
B) 10.4 m
C) 16.4 m
D) 38.8 m
____ 23. Determine the length of DE to the nearest tenth of a centimetre.
D
11.3 cm
E
32°
A) 13.3 cm
F
B) 21.3 cm
C) 6.0 cm
D) 18.1 cm
____ 24. From the start of a runway, the angle of elevation of an approaching airplane is 17.5. At this time, the plane
is flying at an altitude of 6.2 km. How far is the plane from the start of the runway to the nearest tenth of a
kilometre?
A) 6.5 km
B) 1.9 km
C) 20.6 km
D) 19.7 km
____ 25. A surveyor made the measurements shown in the diagram. Determine the distance from R to S, to the nearest
hundredth of a metre.
Q
S
38.91 m
56.5°
R
A) 46.66 m
B) 70.50 m
C) 25.75 m
D) 58.79 m
____ 26. A ladder is 8.0 m long. It leans against a wall. The angle of inclination of the ladder is 72. To the nearest
tenth of a metre, how far from the wall is the base of the ladder?
A) 2.6 m
B) 7.6 m
C) 25.9 m
D) 2.5 m
____ 27. A guy wire is attached to a tower at a point that is 7.5 m above the ground. The angle of inclination of the
wire is 67. Determine the length of the wire to the nearest tenth of a metre.
A) 18.7 m
B) 20.2 m
C) 8.1 m
____ 28. Solve this right triangle. Give the measures to the nearest tenth.
D) 7.9 m
U
6.5.0 cm
V
13.0 cm
W
A)
B)
cm C)
cm D)
cm
cm
____ 29. Solve this right triangle. Give the measures to the nearest tenth.
F
8.0 m
23°
G
H
A)
B)
m
m
C)
D)
m
m
____ 30. The front of a tent has the shape of an isosceles triangle with equal sides 177 cm long. The measure of the
angle at the peak of the tent is 105. Calculate the maximum headroom in the tent to the nearest centimetre.
105°
177 cm
A) 140 cm
177 cm
B) 136 cm
C) 108 cm
D) 250 cm
____ 31. Determine the perimeter of an equilateral triangle with height 9.8 cm. Give the measure to the nearest tenth of
a centimetre.
A) 55.4 cm
B) 33.9 cm
C) 25.5 cm
____ 32. Determine the length of RS to the nearest tenth of a centimetre.
D) 58.8 cm
R
5.7 cm
Q
54°
S
41°
T
A)
cm
B)
cm
C)
cm
D)
cm
D)
cm
____ 33. Determine the length of MN to the nearest tenth of a centimetre.
K
L
53°
M
8.9 cm
35°
N
A)
cm
B)
cm
C)
cm
____ 34. Two trees are 60 yd. apart. From a point halfway between the trees, the angles of elevation of the tops of the
trees are measured. What is the height of each tree to the nearest yard?
tree
tree
36°
31°
60 yd.
A) 37 yd.; 35 yd.
B) 22 yd.; 18 yd.
C) 41 yd.; 50 yd.
D) 41 yd.; 49 yd.
____ 35. From the top of an 90-ft. building, the angle of elevation of the top of a taller building is 49 and the angle of
depression of the base of this building is 65. Determine the height of the taller building to the nearest foot.
49°
65°
90 ft.
A) 248 ft.
B) 112 ft.
C) 128 ft.
D) 325 ft.
____ 36. Calculate the measure of ABC to the nearest tenth of a degree.
A
13 cm
9 cm
B
D
3 cm
C
A)

B) 116.1
____ 37. Determine the area of
C) 63.9
D)

to the nearest square centimetre.
R
21°
23.3 cm
T
A) 291 cm2
S
B) 707 cm2
C) 104 cm2
D) 208 cm2
Short Answer
38. Determine the height of this isosceles triangle to the nearest tenth of a centimetre.
17°
|
|
18.0 cm
39. Determine the length of WX to the nearest tenth of a centimetre.
W
7.5 cm
32°
Z
X
28°
Y
40. Calculate the measure of ABC to the nearest degree.
B
9 cm
A
8 cm
11 cm
C
41. Francis wants to know the distance between the points where two guy wires are attached to a pole. The guy
wires are anchored to the ground at the same point, 9.0 m from the base of the pole. The angle of inclination
of the longer wire is 61° and the angle of inclination of the shorter wire is 44°. To the nearest tenth of a metre,
how far apart are the points where the guy wires are attached to the pole?
42. From the roof of Yee’s building, the angle of elevation of the top of a taller building is 35°. The angle of
depression of the base of the building is 26°. The buildings are 18 m apart. Determine the height of the taller
building to the nearest metre.
43. Solve this right triangle. Give the measures to the nearest tenth.
L
M
19.9 cm
57°
N
44. Solve this right triangle. Give the measures to the nearest tenth.
D
9.1 cm
26°
F
E
Problem
45. In the diagram below, a Coast Guard patrol boat is at C, which is 11.7 km south of Point Atkinson lighthouse.
A sailboat in distress is at A, which is 8.8 km west of the lighthouse.
a) How far is the patrol boat from the sailboat, to the nearest tenth of a kilometre?
b) At what angle to BC should the patrol boat travel to reach the sailboat? Give the answer to the nearest tenth
of a degree.
A
8.8 km
B
11.7 km
C
46. Determine the measures of
and
5
D
to the nearest tenth of a degree.
C
8
A
B
47. A guy wire is connected from a tower to the ground. Determine the height of the tower, to the nearest tenth of
a metre. What assumptions about the ground are you making?
A
51°
E 30.1 m
D
48. Determine the area of ABC to the nearest tenth of a square unit. Determine its perimeter to the nearest tenth
of a unit.
C
59°
23.1
A
B
49. Sue used a clinometer to sight the top of a tall building from a point 120.0 m from the base of the building.
The angle shown on the protractor was 48°. Sue held the clinometer 1.7 m above the ground. Determine the
height of the building to the nearest tenth of a metre.
50. Guy wires are attached to buildings as shown. A student says the angles of inclination of the wires are the
same. Is the student correct? Justify your answer.
51 m
46 m
34 m
37 m
51. Determine the perimeter of this triangle to the nearest tenth of a centimetre.
A
\
/
9.0 cm
34°
B
C
D
52. Solve LMN. Give the measures to the nearest tenth. Explain your strategy.
M
L
4.9 cm
8.1 cm
N
53. A Girl Guide measured the angle of elevation of the top of a monument as 57 The height of the monument is
48.5 m. She then walked 46.0 m due west from the point where she measured the angle of elevation.
Determine the angle of elevation of the monument from her new location to the nearest tenth of a degree.
48.5 m
57°
46.0 m
54. Determine the area of this triangle to the nearest tenth of a square centimetre.
21.5 cm |
135°
|
55. Determine the area of this right triangle to the nearest square metre.
L
850 m
57°
M
N
Unit 2 - Review for Midterm Exam
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
C
A
B
C
A
D
D
A
C
D
C
D
C
A
D
C
A
C
A
C
B
A
B
C
B
D
C
B
D
C
B
D
A
B
C
D
C
SHORT ANSWER
38. 17.8 cm
39.
40.
41.
42.
43.
13.5 cm
92
7.5 m
21 m
MN = 10.8 cm
LM = 16.7 cm
L = 33.0
44. EF = 18.7 cm
DF = 20.8 cm
D = 64.0
PROBLEM
45. a)
Use the Pythagorean Theorem in right ABC.
The Coast Guard patrol boat is approximately 14.6 km from the sailboat.
b)
Use the tangent ratio in right ABC.
The patrol boat should travel at an angle of approximately 36.9 to BC to reach the sailboat.
46. Determine the measure of
in right BDC.
Determine the measure of
.
47. In right AED, side DE is opposite A and AE is adjacent to A.
Solve the equation for AE.
The height of the tower is approximately 24.4 m.
I am assuming the ground is horizontal.
48. Determine the length of AB.
In right ABC, AB is opposite C and BC is adjacent to C.
Solve the equation for AB.
Find the area of ABC.
The area of ABC is approximately 444.0 square units.
Determine the length of AC.
Use the Pythagorean Theorem in right ABC.
The perimeter of ABC is:
The perimeter of ABC is approximately 106.4 units.
49. Sketch and label a diagram to represent the information in the problem.
In right ABC, BC is opposite A and AC is adjacent to A.
The angle between the horizontal and the line
B
of sight is:
A
42°
120.0 m
C
1.7 m
D
Solve this equation for BC.
Find the height, h, of the building.
The height of the building is approximately 109.7 m.
50.
C in right ABC is the angle of inclination
of the guy wire attached to the shorter
building.
D
A
51 m
In right ABC:
46 m
34 m
B
C
E
37 m
F
The angle of inclination of the guy wire attached to the shorter building is approximately 47.7°.
F in right DEF is the angle of inclination of the guy wire attached to the taller building.
In right DEF:
The angle of inclination of the guy wire attached to the taller building is approximately 43.5°.
The student is not correct. The angles of inclination are different.
51. In right ACD, AD is the hypotenuse, AC is opposite D, and CD is adjacent to D. To determine the
length of AD, use the sine ratio.
Solve this equation for AD.
To determine the length of CD, use the cosine ratio.
Solve this equation for CD.
Since AD = AB and CD = BC, the perimeter, P, of the triangle is:
he perimeter of the triangle is approximately 58.9 cm.
52. Determine the length of LM first.
Use the Pythagorean Theorem in right LMN.
LM is approximately 6.4 cm.
Determine the measure of N.
Since MN is adjacent to N and LN is the hypotenuse, use the cosine ratio.
N is approximately 52.8° and L is approximately 37.2°.
53. Label a diagram.
Use right ACD to calculate the length of
CD. AD is opposite ACD and CD is
adjacent to ACD.
So, use the tangent ratio.
A
48.5 m
C 57°
B
46.0 m
Use right ABD to calculate the measure of B.
First determine the length of BD.
D
Determine the measure of B.
AD is opposite B and BD is adjacent to B.
So, use the tangent ratio.
he angle of elevation of the monument from the new location is approximately 32.0.
54. Label a diagram.
ABD is an isosceles triangle, so each base
angle is:
A
21.5 cm |
B
135°
22.5°
Determine the height, AC, of the triangle.
In right ABC, AC is opposite B and AB is
the hypotenuse.
So, use the sine ratio in ABC.
Determine the length of the base, BD, of ABD
BD = 2(BC)
In right ABC, BC is adjacent to B and AB is the hypotenuse.
So, use the cosine ratio in ACB.
|
22.5°
C
D
The base, BD, is:
The formula for Area, A, of a triangle is:
The area of the triangle is approximately 163.4 cm2.
55. In right LMN, LN is the hypotenuse, LM is opposite N, and MN is adjacent to N. Use the sine ratio to
determine the height of the triangle, LM.
Solve this equation for LM.
Use the cosine ratio to determine the length of MN, the base of the triangle.
Solve this equation for MN.
Use the formula for the area, A, of a triangle.
The area of the triangle is approximately 165 009 m .