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L.O. All will be able to remember the sine rule Most can find missing angles using Cosine Rule Some can find missing sides using Cosine Rule Trigonometry

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Page 1: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

L.O.All will be able to remember the sine rule

Most can find missing angles using Cosine Rule

Some can find missing sides using Cosine Rule

Trigonometry

Page 2: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

Starter:

Page 3: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

Calculate the size of angle b giving your answer to 2 decimal places.

Starter:

Page 4: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

L.O.All will be able to remember the sine rule

Most can find missing angles using Cosine Rule

Some can find missing sides using Cosine Rule

Trigonometry 2

Page 5: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

What about...?

Calculate the length of AC giving your answer to 3 significant figures.

Calculate the size of angle a giving your answer to 1 decimal place.

Page 6: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

Cosine Rule

What information do we need to apply the Cosine Rule?

Page 7: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

Circle if we can apply the Cosine Rule

Page 8: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise
Page 9: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

L.O.All will be able to remember the sine rule

Most can find missing angles using Cosine Rule

Some can find missing sides using Cosine Rule

Trigonometry 2

Page 10: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

Find the length of each side marked with a letter

ExtensionCreate and draw your own non right triangle problem that requires the Cosine Rule to calculate missing sides. Give this to the person next to you to answer. Mark their work.

Page 11: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

Missing Side Solutions

a = 9.88 cm

b = 9.03cm

c = 10.8 cm

d = 8.01 cm

Page 12: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

L.O.All will be able to remember the sine rule

Most can find missing angles using Cosine Rule

Some can find missing sides using Cosine Rule

Trigonometry 2

Page 13: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

We need to make angle A the subject

What is the inverse of cos?

Page 14: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise
Page 15: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

ExtensionCreate and draw your own non right triangle problem that requires the Cosine Rule to calculate missing angles. Give this to the person next to you to answer. Mark their work.

Page 16: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

Missing Angle Solutions

a = 35.9o

b = 64.5o

c = 26.2o

d = 29.3o

Page 17: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

L.O.All will be able to remember the sine rule

Most can find missing angles using Cosine Rule

Some can find missing sides using Cosine Rule

Trigonometry 2

Page 18: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise
Page 19: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise
Page 20: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

GCSE QUESTION

Page 21: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

GCSE QUESTION

Page 22: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

L.O.All will be able to remember the sine rule

Most can find missing angles using Cosine Rule

Some can find missing sides using Cosine Rule

Trigonometry 2

Page 23: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

Real Life Question

Page 24: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise
Page 25: Trigonometry L.O. › uploads › 2 › 4 › 2 › 1 › ... · Trigonometry 2. Real Life Question. An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise

An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise. It flies 530 miles North to a point (P) as shown, It then turns left and flies to a point (Q), 670 miles away. Finally it flies back to base, a distance of 520 miles.

Find the bearing of Q from point P.

P

670 miles

W

530 miles

Q

520 miles