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Geometry in two dimensions
Right angled Trigonometry
Non-right angled Trigonometry: The Sine Rule and the Cosine Rule

 

MATH STUDIES

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Geometry and Trigonometry

Worked Examples

 

Question 1

Given the triangle ABC as shown

Ana (A) and Bill (B) left Carol's (C) house at the same time, Ana travelled North at 50km/h and Bill travelled East at 80Km/h.

  1. Represent this information with a suitable diagram.

  2. Calculate their distance apart after 5 hours. (Correct to 3 significant figures)

  3. Calculate the angle between Ana, Bill and Carole's house after 5 hours. (To the nearest degree)

 

First sketch the triangle with the information given

  1. (Diagram not to scale)

    diagram1

  2. AB2 = 4002 + 2502    AB  formula1= 472km

  3. formula2

 

Question 2

Triangle PQR has sides PQ = 8cm, PR = 10cm and QR = 13cm. Calculate all the unknown angles

(Diagram not to scale)

diagram2

 

  1. equation3

  2. To find angle Q we can use the sine or cosine rule

    equation5

    equation6

    equation7

  3. Hence angle R = 180 - 91.8 - 50.3 = 37.9°

 

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