Applications

1
Applications

• Trigonometry
• MATH 103
• S. Rook

2
Overview

• Section 2.4 in the textbook
• Angle of elevation and angle of depression
• Bearing

3
Angle of Elevation and Angle of Depression
4
Angle of Elevation and Angle of Depression

• Angle of Elevation angle
• measured from the
• horizontal (or flat line)
• upwards
• Angle of Depression angle
• measured from the
• horizontal (or flat line)
• downwards

5
Angle of Elevation (Example)

• Ex 1 A ladder is leaning against the top of a
  7-foot wall. If the bottom of the ladder is 4.5
  feet from the wall, what is the angle of
  elevation of the ladder from the ground?

6
Angle of Depression (Example)

• Ex 2 A person who is standing on top of a
  15-foot high sand pile wishes to estimate the
  width of the pile. He visually locates two rocks
  on the ground below at the base of the sand pile.
  The rocks are in the same vertical plane. If
  the angles of depression from the top of the sand
  pile to each of the rocks are 27 and 19, how
  far apart are the rocks and thus what is the
  estimated length of the sand pile?

7
Bearing
8
Bearing

• Bearing the acute angle formed by first
  referencing the north-south line of a compass
  followed by a position east or west
• 4 possibilities for bearing based on the 4
  quadrants in the Cartesian Plane
• Used frequently in navigation and surveying

9
Bearing (Continued)
10
Bearing (Continued)
11
Bearing (Example)

• Ex 3 A boat travels on a course of bearing N
  47.5 E for 74 miles. How many miles north and
  how many miles east has the boat traveled?

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Bearing (Example)

• Ex 4 A man wandering the desert walks 2.3 miles
  in the direction of S 15 W. He then turns 90
  and walks 2 miles in the direction N 75 W. At
  that time, how far is he from his starting point
  and what is his bearing from his starting
  location?

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Summary

• After studying these slides, you should be able
  to
• Set up and solve application problems dealing
  with right triangles
• Additional Practice
• See the list of suggested problems for 2.4
• Next lesson
• Reference Angle (Section 3.1)