Loading...

PPT – Trigonometry PowerPoint presentation | free to download - id: 4240a6-YWQyY

The Adobe Flash plugin is needed to view this content

Trigonometry

- Right angled triangles

A triangle

Opposite and Adjacent are relative to the angle

- The 4cm side is opposite to A
- The 6cm side is adjacent to A
- The 6cm side is opposite to B
- The 4cm side is adjacent to B

SOH CAH TOASine, Cosine Tangent of an angle

SOH CAH TOA

- SOH
- Some Old Houses
- (Sine of angle Opposite side / Hypotenuse)
- CAH
- Creak And Howl
- (Cosine of angle Adjacent side / hypotenuse)
- TOA
- Through Out Autumn
- (Tangent of angle Opposite side / adjacent side)

TOA SOH CAH

- TOA
- Toms Old Auntie
- Tangent of angle Opposite side / adjacent side
- SOH
- Sat On Him
- Sine of angle Opposite side / Hypotenuse
- CAH
- Cursing At Him
- Cosine of angle Adjacent side / hypotenuse

SOH CAH TOA

- SOH

S

O

H

Opposite side sin (x) times hypotenuse

Hypotenuse opposite side divided by sin (x)

Sin (x) opposite side divided by hypotenuse

SOH CAH TOA

C

A

- CAH

H

Adjacent side cos (x) times hypotenuse

Hypotenuse adjacent side divided by cos (x)

Cos (x) adjacent side divided by hypotenuse

SOH CAH TOA

A

- TOA

T

O

Opposite side tan (x) times adjacent side

Adjacent side opposite side divided by tan (x)

tan (x) opposite side divided by adjacent side

Problems for trig

- A stage, is to be built for a concert, it has to

be 2m high so the audience can see the show. - The equipment needs to be pushed up onto the

stage. Health and safety rules say that a ramp

must have a slope of no more than 15 degrees. - The crew need to work out how far away from the

stage to start building the ramp.

m

- A stage, is to be built for a concert, has to be

2m high so the audience can see the show. - The equipment needs to be pushed up onto the

stage. Health and safety rules say that a ramp

must have a slope of no more than 15 degrees. - The crew need to work out how far away from the

stage to start building the ramp.

m

Put answer in context The ramp must start from

at least 7.5m away from the stage

From take-off, an aeroplane climbs at an angle of

20o. When the aeroplane has flown 10km, what

height has it reached?

km

Distance from ground.

Looking for opposite (distance from ground) got

hypotenuse. Must be Sine formula triangle

km

Distance from ground.

Distance from ground sin (20) x 10 3.42 km

from the ground

A plane flies 300km on a bearing of 132 0 from an

airport. How far south and east is it from the

airport. Give answer correct to 3 s.f.

North is always straight up your page for these

questions.. Bearings are always measured from

north around in a clockwise direction.

Draw the problem and work out the angle at AThen

choose which side you want to find first then

choose the formula triangle to suit.

Distance South firstlooking for adjacent side

therefore use cosine formula triangle

Distance East looking for opposite side

therefore use the sine formula triangle

Ratio just means the number you get when you

divide one number by another

Similar shapes have the same angles so they

have the same angle ratios.

Sin(30) is always the same number no matter what

size the opp or hyp

A

Cos(30) is always the same number no matter what

size the adj or hyp

A1

A2

Tan(30) is always the same number no matter what

size the opp or adj

B

C1

C2

C

Sine ratioSin(x)opp / hyp

4.3 / 8.42 ?

To find the angle (x) when you know sin (x) use

the calculator inverse sine function (sin-1)

- Sin (x) 0.86
- x Sin-1 (0.86) 59 0
- Sin (x) 0.35
- x Sin-1 (0.35) 21 0
- Sin (x) 0.45 , what is x ?
- Sin (x) 0.91, what is x?

27 0

66 0

Cosine ratiocos(x) adj / hyp

Cos(30) 0.86

16/18.46?

To find the angle (x) when you know cos (x) use

the calculator inverse cosine function (cos-1)

- Cos (x) 0.86
- x Cos-1 (0.86) 31 0
- Cos (x) 0.35
- x Cos-1 (0.35) 70 0
- Cos (x) 0.45 , what is x ?
- Cos (x) 0.91, what is x?

63 0

24 0

Tangent ratiotan(x) opp / adj

Tan(30) 0.58

7.58 / 13 ?

To find the angle (x) when you know tan (x) use

the calculator inverse tangent function (tan-1)

- tan (x) 0.86
- x tan (0.86) 41 0
- tan (x) 0.35
- x tan-1 (0.35) 19 0
- tan (x) 0.45 , what is x ?
- tan (x) 0.91, what is x?

24 0

42 0

A tourist lift to the top of a cliff travels 23m

from ground to the top of the cliff. The height

from ground to the top of the cliff is 20m what

is the angle of elevation?

Choose a formula triangle

Sketch the problem

We have opposite and hypotenuse must be sine

formula triangle

Looking for the angle BAC.Work out the sine of

the angle BAC then use inverse sine to get angle.

Health and Safety stipulates that a ladder held

up at the side of a wall must have an angle of

elevation between 700 and 800 to be considered

safe. The height to be reached is 2.4m but the

only ladder available is 4.9m will it be classed

as safe?

Not safe

Find angles A and B?We know all sides so ANY

formula triangle will be ok to use.

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)