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Unit 35 Trigonometric Problems

Unit 35 Trigonometric Problems. Unit 35. 35.1 Finding Angles in Right Angled Triangles. Example 1 Find the angle θ in triangle. Solution. ?. ?. ?. , and using on a calculator. SIN. INV. ?. to 1 decimal place. Example 2 Find angle θ in this triangle.

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Unit 35 Trigonometric Problems

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  1. Unit 35Trigonometric Problems

  2. Unit 35 35.1 Finding Angles in Right Angled Triangles

  3. Example 1 Find the angle θ in triangle. Solution ? ? ? , and using on a calculator SIN INV ? to 1 decimal place

  4. Example 2 Find angle θ in this triangle. Solution ? ? ? TAN INV , and using on a calculator ? to 1 decimal place

  5. Example 3 • For the triangle shown, calculate • QS, • x, to the nearest degree Solution (a) Hence (b) ? ? ? ? ? ? ? to the nearest degree ?

  6. Unit 35 35.2 Problems Using Trigonometry 1

  7. When you look up at something, such as an aeroplane, the angle between your line of sight and the horizontal is called the angle of elevation. Similarly, if you look down at something, then the angle between your line of sight and the horizontal is called the angle of depression.

  8. Example A man looks out to sea from a cliff top at a height of 12 metres. He sees a boat that is 150 metres from the cliffs. What is the angle of depression Solution The situation can be represented by the triangle shown in the diagram, where θ is the angle of depression. Using ? ? ? ? to 1 decimal place

  9. Unit 35 35.3 Problems using Trigonometry 2

  10. Example • A ladder is 3.5 metres long. It is placed against a vertical wall so that its foot is on horizontal ground and it makes an angle of 48° with the ground. • Draw a diagram which represents the information given. • Calculate, to two significant figures, • (i) the height the ladder reaches up the wall • (ii) the distance the foot of the ladder is from the wall. • (c) The top of the ladder is lowered so that it reaches 1.75m up the wall, still touching the wall. Calculate the angle that the ladder now makes with the horizontal. Solution • Draw a diagram to represent this information (c) The angle the ladder now makes with the horizontal: (b) (i) Height ladder reaches up the wall: ? ? ? ? ? ? ? ? ? ? ? ?

  11. Unit 35 35.4 Sine Rule

  12. In the triangle ABC, the side opposite angle A has length a, the side opposite B has length b and the side opposite angle C has length c. The sine rule states that Example Find the unknown angles and side length of this triangle Solution Using the sine rule Hence ? As angles in a triangle sum to 180°, then angle ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

  13. Unit 35 35.5 Cosine Rule

  14. The cosine rule states that Example Find the unknown side and angles of this triangle Solution Using the cosine rule, To find the unknown angles, ? ? ? ? ? ? ? ? ? ? So and ? ? to 2 decimal place ? ? ? ? ?

  15. Unit 35 35.6 Problems with Bearings

  16. The diagram shows the journey of a ship which sailed from Port A to Port B and then Port C Port B is located 32km due West of Port A Port C is 45km from Port B on a bearing of 040° • Calculate the bearing of port C from Port A, to 3 significant figures. • The bearing of C from A is • 270° + angle BAC • Using the sine rule, • Calculate, to 3 significant figures, the distance AC. • Using the cosine rule, ? ? ? ? ? ? ? ? ? ? to 3 significant figures ? ? ? ?

  17. The diagram shows the journey of a ship which sailed from Port A to Port B and then Port C Port B is located 32km due West of Port A Port C is 45km from Port B on a bearing of 040° (c) So angle and the bearing of C from A is ? ? ?

  18. Unit 35 35.7 Trig Functions

  19. Note that for any angle θ Also, there are some special values for some angles, as shown below

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