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GCSE: Non-right angled triangles

GCSE: Non-right angled triangles. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Last modified: 2 nd November 2013. Recap. We’ve previously been able to deal with right-angled triangles, to find the area, or missing sides and angles. 5. 6. 3. 4. Area = 15. ? . 30.96 °. ? . 5. 5. 3.

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GCSE: Non-right angled triangles

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  1. GCSE: Non-right angled triangles Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 2nd November 2013

  2. Recap We’ve previously been able to deal with right-angled triangles, to find the area, or missing sides and angles. 5 6 3 4 Area = 15 ? 30.96° ? 5 5 3 ?

  3. Learning Objectives There’s 2 things you’ll need to be able to do: 3cm ? ? 59° 7cm How do I find the area of this non-right angled triangle? How would I find the missing side and angle? We’ll revisit this later...

  4. Area of Non Right-Angled Triangles 3cm Area = 0.5 x 3 x 7 x sin(59) = 9.00cm2 ? 59° 7cm ! Area = Where C is the angle wedged between two sides a and b.

  5. In pairs, work out the areas... Q1 Q2 5 1 3 1 100° 8 Area = 7.39 ? 1 Area = √3 / 4 ? Q3 Q4 3.6 5 3.8 75° 70° 5.2 Area = 9.04 ? Area = 8.03 ?

  6. A* Area Questions ? ?

  7. A* Area Questions Area of sector = Area of triangle = Area of shaded = ?

  8. The Sine Rule For this triangle, try calculating each side divided by the sin of its opposite angle. What do you notice in all three cases? b c 65° 5.02 A 10 ? We can see the following: 85° B C 30° 9.10 a

  9. Examples 8 Q1 Q2 8 50° 85° 100° 45° 15.76 ? 30° 11.27 ? 5 Q4 8 Q3 126.42° ? 85° 30° 10 6 56.12° ? Bro Tip: When you have a missing angle, it’s better to ‘flip’ your formula to get i.e. in general put the missing value in the numerator.

  10. Exercises Find the missing angle or side. Please copy the diagram first! Give answers to 3sf. Q1 Q2 Q3 ? ? ? Q4 Q6 Q5 ? ? ?

  11. Cosine Rule The sine rule could be used whenever we had two pairs of sides and opposite angles involved. However, sometimes there may only be one angle involved. We then use something called the cosine rule. Cosine Rule: (This formula is provided in the exam, but you should remember it) Bro Tip: It’s helpful to label first your angle as and the opposite side as . ?

  12. Try these… e.g. 1 e.g. 2 e.g. 3 ? ? ?

  13. Exercises Use the cosine rule to determine the missing angle/side. Quickly copy out the diagram first. ? ? ? ? ? ?

  14. A* GCSE Questions Q2 Q1 ? ?

  15. A* GCSE Questions What is the area of the triangle? ?

  16. Sin or Cosine Rule? If you were given these exam questions, which would you use?  Sine Sine  Cosine   Cosine  Sine  Sine  Cosine Cosine 

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