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Trigonometry

- Section 3 Solve Application Problems using

Right Triangle Trigonometry

Applications

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

Terminology

- Angle of Elevation

?

Terminology

- Angle of Depression

?

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.

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

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

Surveying

Application Surveying

Example 3 of 4

D 52.7 ft

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?

Practice Set 17

- Pages 59-61

Trigonometry - Section 3

- Solving problems with no right triangles.

Review

Example 1

- Determine the height of this isosceles triangle.

height ?

40 ?

15 ft

h 6.3 ft

Example 2

- Determine the length of side x in this

equilateral triangle.

height 48

x

x 55.4

Practice Set 18

- Page 64 - 65

Trigonometry Section 3

- Additional Technical Applications

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

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

Application 3

- Determine the taper angle of this steel shaft.

A

t

?t 7.1?

22 mm

40 mm

145 mm

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

Application 4

x 4.16

x

radius 2.4

Terminology Tangent

- Tangent Line

tangent point

tangent line

Property

radius

90?

Angle outside a circle

34?

Putting it all together

1.4 ft dia.

0.7 ft radius

40?

0.7 ft

20?

Example Illustration

0.8 dia.

0.4

64?

32?

Example Illustration

0.5 dia.

0.25

18?

36?

Example Solve

- A gauge pin is placed in a machined groove as

shown. Determine the length of dimension x.

8 mm dia.

32?

x

Example Solve

8 mm dia.

32?

x

x 6.4 mm 4 mm 10.4 mm

Piston Travel

290?

Piston Travel

1.75 0.599 1.151

?

70?

0.599

290?

Practice Set 19

- Pages 73-75

Whats Next?

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

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