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
Find the unknown angle, show working
TOA


opposite
adjacent
17
tan  
29
tan  


= tan  17
29 
= 30.379…
= 30 22 44.85
1

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What have we learnt?
About SOH CAH TOA
How to find the length of an unknown side
How to find an unknown angle
Where to now?
How to round our angle measure
To use our knowledge in solving real life
problems




Angles are measured in degrees
Degrees can be divided into smaller units
There are 60 minutes in 1 degree (minute
symbol is )
And there are 60 seconds in 1 minute
(second symbol is )


On your calculator, we use the
button to
convert a decimal answer into degrees,
minutes and seconds.
For example: 45.2514
◦ Becomes 45 15 5.04
◦
◦
◦
◦
◦
degrees minutes seconds
Remember that there are 60 seconds in a minute
We can round our result to the nearest minute
5
45 15 (to nearest minute)
45 (to nearest degree)
round leave
up
same
30
15

Example 2: 30.75978
◦ Becomes 30 45 35.21
◦
degrees minutes seconds
◦ 30 46 (to nearest minute)
◦ 31 (to nearest degree)
45 round leave
up
35
same
30

Convert 70.6231 to degrees, minutes,
seconds and round to the nearest minute
◦ 70 37 23.16

Convert 26.565 to degrees, minutes, seconds
and round to the nearest minute
◦ 26 33 54

= 70 37
 5 
cos 1 

11


Find
degree
◦ 62 57 51.51
= 26 34
and round to the nearest
= 63

Angle of elevation is the angle of looking up,
measured from the horizontal.

Angle of depression is the angle of looking
down, measured from the horizontal.
TOA
h
tan 18 
600
h  600  tan 18

h  194.9518177
h  195 m (to the nearest metre)
There are many different ways to approach
this question.
115
tan 22 
d
115
d
tan 22
d  284.6 metres (to 1 dec. pl.)



Practical problems: ex 14D Q4,5,6 (pg 504)
Using angles of elevation & depression in
application: Complete any 5 questions from
ex14G (pages 518,519)
◦ If you would like to see more worked examples see
page 516 and page 518 of your textbook