1. Reviewing Trig Ratios 7.4 Chapter 7 Measurement 7.4.1
MATHPOWERTM 10, WESTERN EDITION
7.4.1

2. Soh Cah Toa The Primary Trigonometric Ratios q Hypotenuse Hypotenuse
Opposite
Opposite
Opposite
Opposite
Opposite
Adjacent q
Adjacent
Adjacent
Adjacent
Adjacent
Opposite
Opposite
Hypotenuse
Opposite
Adjacent
Sine q =
Tan q =
Soh Cah Toa
Adjacent
Hypotenuse
Cosine q =
7.4.2

3. Determining Values of Primary Trigonometric Ratios
7.4.3

4. Trigonometric Ratios of Acute Angles
Find each of the following, to three decimal places:
a) sin 640 =
b) cos 280 =
c) tan 480 =
0.899
d) tan 140 =
e) sin 590 =
f) cos 820 =
0.249
0.857
0.883
1.111
0.139
Find the measure of each angle, to the nearest degree:
190
d) tan A =
e) sin B =
f) cos C = 2
370
a) sin A =
b) cos B =
c) tan C =
330
490
510
undefined
7.4.4

5. Finding the Length of an Unknown Side
x = 16 Tan 34
x = 10.8 cm
y = 19.3 cm
x = 27 sin42
x = 18.1 cm
y = 27 cos42
y = 20.1 cm
7.4.5

6. Find the Measure of the Unknown Angle
c2 = a2 + b2
262 = x
x2 =
x2 = 315
x = 17.7 cm
q = 43.00
c2 = a2 + b2
x2 =
x2 = 680
x = 26.1 cm
q = 32.50
7.4.6

7. Solving a Right Triangle To solve a right angle triangle means
to find all missing sides and angles. A
510 x y
x = 33.5 cm
y = 21.1 cm B C
26 cm
AB = 33.5 cm
AC = 21.1 cm
B = 390
7.4.7

8. 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.
x = 12 sin 68
x = m
The tree is m tall.
7.4.8

9. 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 x
x = 12 cos360
x = 9.71 m
The wall is 9.71 m high.
7.4.9

10. Solving Problems Involving Trigonometry- Problem 3
Find the height of the cliff.
y = 70 cos500
y = 45.0 m x 45
x = 45 Tan400
x = m y
The cliff is
37.76 m high.
7.4.10

11. Assignment Suggested Questions: Page 329 Page 332 4 1, 2
4 1, 2
Page 332
1, 2, 6, , 17