Transcript Bearings

0 Introduction
0 What are bearings?
0 Application in Triangle Trigonometry
0 Application in Real Life
0 Sample Questions
0 Activity (Try it yourself!)
0 Question and Answer
0 What are bearings?
0 From Wikipedia,
0 A bearing is the angle between a line connecting two
points and a north-south line.
Key concepts
0 Just a quick revision of the three functions
0 Sine function (sin), defined as the ratio of the side
opposite the angle to the hypotenuse.
0 Cosine function (cos), defined as the ratio of the
adjacent leg to the hypotenuse.
0 Tangent function (tan), defined as the ratio of the
opposite leg to the adjacent leg.
Application in Triangle
0 To cut a long story short, a bearing is the direction
from one object to another. In air navigation, bearings
are given as angles rotated clockwise from the north.
Application in Triangle
0 A ship travels on a N50° E course. The ship travels
until it is due north of a port which is 10 nautical miles
due east of the port from which the ship originated.
How far did the ship travel?
0 The angle opposite d is the complement of 50°,
which is 40°. Therefore we can find d using the
Cosine Function
0 Cos40=a/h=10/d
0 D(cos)40=10
0 D=10/cos40=13.05 approx.
Application in Real Life
0 In Real Life, bearings are commonly used in three
forms of navigation:
0 Marine Navigation
0 Aircraft Navigation
0 Land Navigation
0 With the help of bearings, soldiers, divers and hikers
alike will not get lost while exploring unknown or
new territory!
Application in Real Life
0 According to the US Army, bearings can also be used
in war-time conditions.
0 Bearings are able to:
0 Determine the location of a foreign object or target
0 Aid piloting of an aircraft
0 Bring a drone from one position to another by remote
0 Search and Rescue a lost soldier
Other Sample Questions
0 The above link will address more queries about the
use of bearings and how bearings work.
0 Bearings 1 through Bearings 3 are sample questions.
Sample Questions
0 This link uses some illustrations to explain the
concept of bearings as well as many examples
0 It covers bearings and directions
Additional Sample Questions
0 The above link also gives more info about bearings
and has an interactive applet for users to apply what
they know of bearings to navigate a ship.
Activity (Try it yourself!)
0 (Bing Wen) Please provide sample questions from
some workbooks that range from easy to challenging
and then paste them here. Get the class to write their
answers on the board and present how they get these