Trigonometry

1
Trigonometry

• Section 3 Solve Application Problems using
  Right Triangle Trigonometry

2
Applications

• Measuring inaccessible lengths
• Height of a building (tree, tower, etc.)
• Width of a river (canyon, etc.)

3
Terminology

• Angle of Elevation

?
4
Terminology

• Angle of Depression

?
5
Application Height
Example 1 of 4

• To establish the height of a building, a person
  walks 120 ft away from the building.
• At that point an angle of elevation of 32? is
  formed when looking at the top of the building.

6
Application Height
Example 1 of 4

• To establish the height of a building, a person
  walks 120 ft away from the building.
• At that point an angle of elevation of 32? is
  formed when looking at the top of the building.

?
H 74.98 ft
7
Application Height
Example 2 of 4
?

• An observer on top of a hill measures an angle of
  depression of 68? when looking at a truck parked
  in the valley below.
• If the truck is 55 ft from the base of the hill,
  how high is the hill?

55 ft
H 136.1 ft
8
Surveying
9
Application Surveying
Example 3 of 4
D 52.7 ft
10
Application Surveying
Example 4 of 4

• Road has a grade of 5.5.
• Convert this to an angle expressed in degrees.

?
5.5 ft
100 ft
A 3.1?
11
Practice Set 17

• Pages 59-61

12
Trigonometry - Section 3

• Solving problems with no right triangles.

13
Review
14
Example 1

• Determine the height of this isosceles triangle.

height ?
40 ?
15 ft
h 6.3 ft
15
Example 2

• Determine the length of side x in this
  equilateral triangle.

height 48
x
x 55.4
16
Practice Set 18

• Page 64 - 65

17
Trigonometry Section 3

• Additional Technical Applications

18
Application 1
d 0.46

• Determine the depth d of the groove machined in
  this steel block.

1.1
1.1
0.8
0.4
d
41?
82?
3
19
Application 2

• Determine the total length of steel needed to
  make this frame.

35?
35?
11 ft
h 3.85 ft, Total 11 ft 6.7 ft 6.7 ft
3.85 ft 28.25 ft
20
Application 3

• Determine the taper angle of this steel shaft.

A
t
?t 7.1?
22 mm
40 mm
145 mm
21
Application 4

• The diagram shows a bolt circle. Determine the
  distance x between the centers of any two bolt
  hole locations.

x


radius 2.4


22
Application 4
x 4.16
x



radius 2.4

23
Terminology Tangent

• Tangent Line

tangent point
tangent line
24
Property


radius
90?

25
Angle outside a circle
34?
26
Putting it all together
1.4 ft dia.
0.7 ft radius
40?
0.7 ft
20?
27
Example Illustration
0.8 dia.
0.4

64?
32?
28
Example Illustration
0.5 dia.

0.25
18?
36?
29
Example Solve

• A gauge pin is placed in a machined groove as
  shown. Determine the length of dimension x.

8 mm dia.

32?
x
30
Example Solve
8 mm dia.

32?
x
x 6.4 mm 4 mm 10.4 mm
31
Piston Travel
290?
32
Piston Travel
1.75 0.599 1.151
?
70?
0.599
290?
33
Practice Set 19

• Pages 73-75

34
Whats Next?

• Quizzes 1 -3
• pages 76 83
• Chapter Test on Trigonometry