362
MathWorks 10 Workbook
CHAPTER TEST, P. 284
1. 5 in, 15 in, 25 in, 35 in, and 60 in
2. x = 7.2 m
CHAPTER 7:
TRIGONOMETRY OF RIGHT TRIANGLES
7.1 THE PYTHAGOREAN THEOREM
BUILD YOUR SKILLS, P. 290
y ≈ 3.5 m
1. a)
3. The river is approximately 42.7 m wide.
Z
4. The man is approximately 2 m tall.
5. When the side lengths of a rectangle are
doubled, the area is quadrupled.
Y
b)
always 60º and the ratios of the sides will
Q
r
s
places, the shapes are similar.
In equilateral triangles, the angles are
z
x
6. When the ratios are rounded to 2 decimal
7. a)True, all equilateral triangles are similar.
X
y
R
S
q
f
c)
D
E
always be equal.
b) False, all isosceles triangles are not similar.
e
The angles do not need to be equal, nor do
d
the sides have to be proportional.
c) True, congruent triangles are similar. The
F
corresponding angles are equal and the
ratios of sides will be 1:1.
d)
8. The scale factor of the projection is about 8.3.
r
S
t
s
9. 17′ is represented by 7.8″.
6′ is represented by 2.8″.
5′ 2″ is represented by 2.4″.
7′ 2″ is represented by 3.4″.
10.The painting will be 31.25 inches by
43.75 inches.
11. 95.7 cm by 126.5 cm
T
R
Answer Key
2. a)
4.
A
c
B
b
a
h
ℓ
C
b)
Q
s
r
R
q
c)
S
Y
x
d
h2 + d2 = ℓ2
5. x =
z 2 − y2
y=
z2 − x2
w
6. x ≈ 8.0 cm
W
d)
X
y
7. approximately 12.5 feet
d
F
y ≈ 6.7 cm
E
8. Your route would be about 83.7 m shorter by
f
e
walking diagonally across the field.
PRACTISE YOUR NEW SKILLS, P. 295
D
1. approximately 10 ft 7.2 in
3. In ΔABC:
2. approximately 14.4 m
a + c = (x + y)
2
2
2
3. approximately 11.1 m
In ΔABD:
4. approximately 41 in
x2 + z2 = c2
5. approximately 50.9 km
In ΔBDC:
z2 + y2 = a2
363
364
MathWorks 10 Workbook
7.2 THE SINE RATIO
7.3 THE COSINE RATIO
BUILD YOUR SKILLS, P. 298
BUILD YOUR SKILLS, P. 310
1. a) sin A ≈ 0.62
b) sin A ≈ 0.54
1. a) cos 23° = 0.9205
2. a) sin 10° = 0.1736
b) sin 48° = 0.7431
sin 67° = 0.9205
c) sin 62° = 0.8829 d) sin 77° = 0.9744
b) cos 83° = 0.1219
3. sin 90° = 1
sin 7° = 0.1219
Possible reasons will vary.
c) cos 45° = 0.7071
4. a) a ≈ 8.2 cm
sin 45° = 0.7071
b) x ≈ 3.8 cm
d) cos 37° = 0.7986
5. about 7 ft
sin 53° = 0.7986
2. a) x ≈ 8.2 cm
6. about 8.6 m
7. a) h ≈ 14.3 mm
c) x ≈ 8.6 cm
b) h ≈ 12.9 cm
b) x ≈ 1.7 cm
d) x ≈ 12.2 cm
3. about 5.4 m
8. approximately 5.3 m long
4. about 9.8 yards
9. about 22 m
5. about 6.2 m
10.about 404.5 m
6. about 14.1 m
11. approximately 203.9 m
7. about 11.6 m
12.about 1.9 m
8. about 502 km
PRACTISE YOUR NEW SKILLS, P. 306
PRACTISE YOUR NEW SKILLS, P. 315
1. a) sin A ≈ 0.6371
b) sin B ≈ 0.7191
1. a) x ≈ 3.6 cm
b) a ≈ 4.8 m
2. a) x ≈ 17.9 cm
b) y ≈ 12.5 cm
c) r ≈ 9.5 cm
d) ℓ ≈ 3.1 m
3. about 5.5 m
2. approximately 17.3 m
4. about 8.6 m
3. approximately 23.7 m
5. about 41.7 m
4. about 1.24 km
5. about 8.49 km
6. about 3.42 m