Find the unknown angle, show working TOA

= = 30.379…

= 30 22 44.85

Quick Quiz

2917tan

tan

adjacentopposite

2917tan 1

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

Trigonometry

All about angles… 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◦ 45 15 (to nearest minute)◦ 45 (to nearest degree)

Rounding angles…

round up

leave

same

30

5

15

Example 2: 30.75978

◦ Becomes 30 45 35.21

◦ degrees minutes seconds

◦ 30 46 (to nearest minute)

◦ 31 (to nearest degree)

Another example…

round up

leave

same

3035

45

Convert 70.6231 to degrees, minutes, seconds and round to the nearest minute◦ 70 37 23.16 = 70 37

Convert 26.565 to degrees, minutes, seconds and round to the nearest minute◦ 26 33 54 = 26 34

Find and round to the nearest degree◦ 62 57 51.51 = 63

Your turn…

115cos 1

Angle of elevation is the angle of looking up, measured from the horizontal.

Angles of Elevation & Depression

Angle of depression is the angle of looking down, measured from the horizontal.

TOA

Examples…..

)(1959518177.194

18tan600600

18tan

metrenearestthetomhhh

h

There are many different ways to approach this question.

Example 2…..

.).1(6.28422tan

115

11522tan

pldectometresd

d

d

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

Practice….