This document outlines lesson 4 on trigonometric application vocabulary. It includes the objective to identify angles of direction and elevation/depression in real-world problems using trigonometry. Key vocabulary terms are defined, like accurate angles, angle of elevation, direction, and examples are provided to demonstrate calculating bearing/heading, horizontal and vertical distances, and true north directions. Students are assigned to complete a foldable with vocabulary on one side and examples on the other, as well as a bearing practice worksheet.

1. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Lesson 4: Trigonometric Application Vocabulary
Interactive Notebook Pages 96-97
Unit 6: Trig Applications

2. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Outline
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and Distance
Ex 2: Horizontal and Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment

3. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Application Vocabulary
Today’s Objective
Students will be able to identify and find angles of direction, angles of
elevation/depression, and other components such as horizontal and vertical
distances of real-world problems using trigonometry.

4. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Accurate Angles
DMS
Degrees-Minutes-Seconds (DMS) are used to give a more precise angle without
a lot of decimal places.
1 Revolution = 360
1 Degree = 60 minutes or 600
1 minute = 60 seconds or 6000

5. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Converting To and From DMS
Examples
Convert 42 2504000 as a decimal.
Convert 132.4963 into DMS.

6. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Angle of Elevation and Depression
Elevation
The angle of elevation (or depression) is the angle made with the HORIZONTAL
up to (elevation) or down to (depression) an object. These angles are also called
inclination (up) and declination (down).

7. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Calculating the Angle of Depression
Example
An observer at the top of a 100-ft light tower spots a whale 982 feet from the
base of the tower. What is the angle of depression to the whale?

8. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Angles of Direction
Directional Angles give a direction to head towards an object.
Bearing/Heading
The BEARING, or heading, gives us a directional angle made with north/south
first, then turning east/west.
North is up, South is down, East is right, and West is left
True North Bearing
A true north bearing gives us a directional angle made with true north in a
CLOCKWISE direction.

9. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Direction Examples
Examples
Sketch the direction of these angles.
I N 52 E
I S 33 E
I 236
I 312

10. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Example 1
A boat leaves port and travels due west for 26 miles and then turns and heads
due south for another 12 miles. What is the bearing and distance from port?

11. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Example 2
A plane flies at a heading of N 42 E for 230 miles. What are the north/south
and east/west distances?

12. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Example 3
An explorer is 250 miles south and 192 miles west of his camp. What is the
true-north bearing he should take to return to camp?

13. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Example 4
A boat sets sail at a heading of 165 at a speed of 2.4 knots (nautical miles per
hour). How far north or south and east or west has the boat sailed after 3 hours?

14. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Making the Foldable
I Cut around the perimeter
I Fold to the center
I Label left side ”Vocab”
I Label right side ”Examples”
I Attach to NOTES SIDE of p. 96-97

15. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
Quick Check
A hot-air balloon is attached to a rope that is 50-ft long. The rope makes an
angle of elevation of 67 . How high o↵ the ground is the balloon?

16. Lesson 4: Vocab
Unit 6: Trig
Applications
Objective
Vocabulary
Accurate Angles
Angle of Elevation
Direction
Examples
Ex 1: Bearing and
Distance
Ex 2: Horizontal and
Vertical Distances
Ex 3: True North
Ex 4: Boat Heading
Conclusion
Foldable
Quick Check
Assignment
The Assignment
Bearing Practice
I Use a blank page folded in 1/4
I Complete all problems (with a sketch)
I Attach to page 96-97 on the PRACTICE SIDE