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Chapter 7 Measurement
7.4
MATHPOWERTM 10, WESTERN EDITION 7.4.1
Adjacent
Opposite
Opposite
The Primary Trigonometric Ratios
Hypotenuse
q
Hypotenuse
q
Adjacent
Sine q =
Opposite
Hypotenuse
Adjacent
Cosine q =
Hypotenuse
Opposite
Tan q =
Opposite
Adjacent
Soh Cah Toa
Quic kTime™ a nd a
GIF d eco mp re sso r
ar e n eed ed to see thi s p ictu re.
7.4.2
Determining Values of Primary Trigonometric Ratios
12
5
13
13
5
13
12
13
12
5
15
5
12
25
20
25
20
15
25
25
15
20
20
15
7.4.3
Trigonometric Ratios of Acute Angles
Find each of the following, to three decimal places:
a) sin 640 = 0.899
d) tan 140 = 0.249
b) cos 280 = 0.883
e) sin 590 = 0.857
c) tan 480 = 1.111
f) cos 820 = 0.139
Find the measure of each angle, to the nearest degree:
0
0
d)
tan
A
=
0.7563
37
19
a) sin A = 0.3214
b) cos B = 0.6541
490
e) sin B = 0.5421
c) tan C = 1.2312
510
f) cos C = 2
330
undefined
7.4.4
Finding the Length of an Unknown Side
opp
Tan q =
adj
x
Tan 34 =
16
Qu ickTi me™ and a
GIF dec omp ress or
are nee ded to se e thi s pic ture .
adj
cosq =
hyp
16
cos 34 =
y
16
y=
cos34
x = 16 Tan 34
x = 10.8 cm
QuickTime™ and a
GIF decompressor
are needed to see this picture.
opp
sinq =
hyp
x
sin42 =
27
x = 27 sin42
x = 18.1 cm
y = 19.3 cm
adj
cosq =
hyp
Qu ickTi me™ and a
GIF dec omp ress or
are nee ded to se e thi s pic ture .
y
cos42 =
27
y = 27 cos42
y = 20.1 cm
7.4.5
Find the Measure of the Unknown Angle
c2 = a2 + b2
262 = x2 + 192
x2 = 262 - 192
x2 = 315
x = 17.7 cm
adj
cosq =
hyp
19
cosq =
26
q = 43.00
QuickTime™ and a
GIF decompressor
are needed to see this picture.
c2 = a2 + b2
x2 = 142 + 222
x2 = 680
x = 26.1 cm
opp
tanq =
adj
14
tanq =
22
q = 32.50
7.4.6
Solving a Right Triangle
To solve a right angle triangle means
to find all missing sides and angles.
A
0
510
x
y
C
26
sin51 =
x
26
x=
sin510
26
tan 51 =
y
0
26 cm
B x = 33.5 cm
B = 1800  (900  510 )
B = 390
Quic kTime™ and a
GIF dec ompress or
are needed to see this pic ture .
26
y=
0
tan51
y = 21.1 cm
AB = 33.5 cm
AC = 21.1 cm
B = 390
7.4.7
Solving Problems Involving Trigonometry- Problem 1
A tree casts a shadow 12 m long.
The angle to the top of the tree
from the end of the shadow is 680.
Find the height of the tree.
opp
Tan q =
adj
x
Tan68 =
12
x = 12 sin 68
x = 11.13 m
The tree is 11.13 m tall.
7.4.8
Solving Problems Involving Trigonometry- Problem 2
A 12 m ladder is leaned up against a brick wall. If the ladder
forms an angle of 360 with the wall, find the height of the wall.
360
12 m
opp
Cosq =
hyp
x
Cos36 =
12
0
x
x = 12 cos360
x = 9.71 m
The wall is 9.71 m high.
7.4.9
Solving Problems Involving Trigonometry- Problem 3
Find the height of the cliff.
y
cos5 0 =
70
0
y = 70 cos500
y = 45.0 m
x
x
Tan40 =
45
0
y
x = 45 Tan400
x = 37.76 m
The cliff is
37.76 m high.
7.4.10
Suggested Questions:
Page 329
4 1, 2
5 1-6
6 1-6
Page 332
1, 2, 6, 8 - 14,
17