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Trigonometry

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Trigonometry

Right angled triangles

- 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
- Some Old Houses
- (Sine of angle =Opposite side / Hypotenuse)

- Some Old Houses
- CAH
- Creak And Howl
- (Cosine of angle = Adjacent side / hypotenuse)

- Creak And Howl
- TOA
- Through Out Autumn
- (Tangent of angle = Opposite side / adjacent side)

- Through Out Autumn

- TOA
- Tom’s Old Auntie
- Tangent of angle = Opposite side / adjacent side

- Tom’s Old Auntie
- SOH
- Sat On Him
- Sine of angle =Opposite side / Hypotenuse

- Sat On Him
- CAH
- Cursing At Him
- Cosine of angle = Adjacent side / hypotenuse

- Cursing At Him

- SOH

S

O

H

Opposite side = sin (x) times hypotenuse

Hypotenuse = opposite side divided by sin (x)

Sin (x) = opposite side divided by hypotenuse

C

A

- CAH

H

Adjacent side = cos (x) times hypotenuse

Hypotenuse = adjacent side divided by cos (x)

Cos (x) = adjacent side divided by hypotenuse

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

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

km

Distance from ground.

km

Distance from ground.

Distance from ground = sin (20) x 10

= 3.42 km from the ground

North is always straight up your page for these questions..

Bearings are always measured from north around in a clockwise direction.

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

C

C1

C2

4.3 / 8.42 = ?

- 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

Cos(30) = 0.86

16/18.46=?

- 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

Tan(30) =0.58

7.58 / 13 = ?

- 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

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