Download Trigonometry Lecture Notes, Section 2.5

Trigonometry Lecture Notes
Section 2.5
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Section 2.5: Further Applications of Right Triangles
Big Idea: You can use trig functions and their definitions to compute angles and distances in
real-world problems.
Big Skill: You should be able to “solve” real world applications by drawing right triangles to
represent the situation and then solving the right triangles.
To solve applied right triangle problems:
1. Make a sketch of the situation.
2. Identify/draw right triangles on your sketch that connect given information to unknown
information.
3. Solve the right triangle or triangles.
Bearing:
In navigation, the word bearing means one of two things:
 An angle measured clockwise from due north. Picture:

An angle measured from either due north or due south in either a clockwise or
counterclockwise direction. The direction is specified as a rotation either to the east or
the west. The starting direction is stated first, then the angle, then the direction of
rotation of that angle from the starting direction. Pictures:
Practice:
1. Radar stations A and B are 8.6 km apart and on an east-west line. Station A detects an
airplane at a point C on a bearing of 53. Station B detects the same airplane on a bearing
of 323. Find the distance of the airplane to both stations.
Trigonometry Lecture Notes
Section 2.5
Page 2 of 5
2. Radar stations A and B are 9.2 km apart and station B is on a bearing of N 76 E relative
to station A. Station A detects an airplane at a point C on a bearing of S 55 E. Station B
detects the same airplane on a bearing of S 35 W. Find the distance of the airplane to
both stations.
Trigonometry Lecture Notes
Section 2.5
Page 3 of 5
3. A road with a 7% grade is 1.2 miles long. How high does the road rise over this length?
4. What is the angle of elevation above the floor of a “body diagonal” across a room that is
15’ by 22’ by 8’?
Trigonometry Lecture Notes
Section 2.5
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5. Suppose you measure the angle of elevation to the top of a building to be 46.7, then you
step back 115’, and measure the new angle of elevation to be 38.2. If your measuring
instrument is 6’ above the ground, what is the height of the building?
Trigonometry Lecture Notes
Section 2.5
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6. The drawing below shows how to use a pin to check the angle of a dovetail cut. Find
dimension x.