1 / 18

Triangle Area Calculation with PLT Skills

Learn how to find the area of a triangle using sine, develop creative mathematical anagrams, and enhance your PLT skills in a real-life context. Start your journey towards effective independent thinking and reflective learning.

eltonday
Download Presentation

Triangle Area Calculation with PLT Skills

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Real life cross/curricular links? Where are we in our journey? Which ones are you using? PLT Skills LESSON OBJECTIVES Always aim high! We are learning to: • Finding connections between different words. (Which PLT skills?) • Accurately finding the area of a triangle using sine. (Grades A/A*) AUTHOR www.mistrymaths.co.uk

  2. Which ones are you using? BRAIN IN GEAR Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills EXAMPLE DITDIONA can be rearranged to make ADDITION TASK Work out the following Mathematical anagrams: Scalene Area Included Angle EXTENSION Develop your own Mathematical anagrams as above as a creative thinker.

  3. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager STARTER PLT Skills TASK Work out x: Find the area of: Write 710000 in standard form 1) 3) 2) 2x + 1 3x - 4 7cm x + 11 2x - 8 5cm 5 7.1 x 10 4cm = 7 6 x 4 2x - 8 x + 11 3x - 4 = 360 2x + 1 + + + = 6cm 10 2 = 360 8x ÷ 8 ÷ 8 = 45° x 3 2 100 EXTENSION Work out x: Value of: 4) 5) x Power - Reciprocal 124° 6m Root 4m 100° Pentagon adds to 540° 1 111° 5m = 90° 6m 3 ) ( 100 10 10 1 1 x = = x Work out x: 3 4 4 5 1000 10 x = 540° - 90° - 124° - 100° - 111° x 5 x = = x = 115° x = 12.5m Area of a triangle = 10m 4m 2 Area of a triangle = 12cm x 5m

  4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills AREA OF A TRIANGLE INTRODUCTION – PROOF B H o a c h θ A C A D b opposite h Area of a triangle = x b x h sin θ = sin θ = a hypotenuse x b a x sin θ x Area of a triangle = h = a x sin θ sin θ a b Area of a triangle = 1 1 1 1 2 2 2 2 a b sin θ Area of a triangle =

  5. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills AREA OF A TRIANGLE EXAMPLE 1 Find the area of the triangle below giving your answer to 3 s.f. : B a 5cm θ 36° C A b 9cm a b sin θ Area of a triangle = x Area of a triangle = x sin x 36° 5 9 2 Area of a triangle = 1 1 1 13.2cm 2 2 2 a b sin θ Area of a triangle =

  6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills AREA OF A TRIANGLE sin θ a c Area of a triangle = A TASK 1 (GRADE A) x x sin Area of a triangle = x 67° 3 1.25 16° 1) Find the areas of the triangles below giving your answers to 3 s.f. : 17cm 14cm (d) Area of a triangle = (c) (a) (b) B C sin θ b c Area of a triangle = x x sin Area of a triangle = x 28° 67 100 Area of a triangle = C 8m (h) (g) (e) (f) sin θ a b Area of a triangle = 67° B A x x sin Area of a triangle = x 35° 8 6 11cm 2 2 2 1 1 1 1 1 1 1 13.8cm 1.73m 1570cm Area of a triangle = 2 2 2 2 2 2 2 C B 67cm a 5cm 28° C 36° B A 1m C A b 9cm a b sin θ Area of a triangle =

  7. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills AREA OF A TRIANGLE EXAMPLE 2 Find the missing side a below giving your answer to 3 s.f. : B a 2 Area = 8.2cm a θ 36° C A 7cm b a b sin θ Area of a triangle = x 7 a x 36 x sin = 8.2 x a x = 3.5 sin 36 8.2 2 1 1 1 1 13.2cm 8.2 2 2 2 2 a = x 3.5 sin 36 a = 3.99cm x sin x 36° 9 x x sin Area of a triangle = x 36° 5 9 5 Area of a triangle = a b sin θ Area of a triangle =

  8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager a b sin θ Area of a triangle = PLT Skills AREA OF A TRIANGLE x 7 a x 36 x sin = 8.2 A 2 TASK 2 (GRADE A) Area = 8352cm x a x = 3.5 sin 36 8.2 55° 1) Find the missing lengths in the triangles below giving your answers to 3 s.f. : c 8.2 2m a = (d) (c) x 3.5 sin 36 (a) (b) a = 3.99cm B C b c sin θ Area of a triangle = x x 6 x c sin 32 = 42 42 x c 3 x = sin 32 C 2 42 Area = 84cm c = x sin 32 3 16cm c = 26.4m (h) (g) (e) (f) 32° B a c sin θ Area of a triangle = A c x c 32 x 54 x sin = 864 1 1 1 1 1 1 1 2 2 2 2 2 2 2 x c x = 16 sin 54 864 864 c = x 16 sin 54 c = 66.7cm B C a 2 Area = 8632cm 5cm C 36° b C A b 9cm 81° a b sin θ Area of a triangle = B A 1m

  9. a 2 Area = 8.2cm a θ 36° Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills AREA OF A TRIANGLE EXAMPLE 3 Find the area of the triangle below giving your answer to 3 s.f. : B Cannot use the formula until we calculate a missing angle for θ c a 14cm a b sin θ Area of a triangle = 10cm A θ A C 20cm Use the cosine rule to find θ b a b sin θ Area of a triangle = b² + c² - a² cos A = b 2bc 2 2 2 10 - 20 14 + = b c sin θ Area of a triangle = cos θ x 2 20 x 10 304 x sin 40.54 x 20 x 10 Area of a triangle = = 2 2 cos θ 1 1 1 1 1 1 1 13.2cm 65.0cm 400 304 x 7 2 2 2 2 2 2 2 a x 36 x sin = = 8.2 θ 400 Area of a triangle = x a x = 3.5 sin 36 8.2 = 40.54° θ - 1 cos 8.2 a = x 3.5 sin 36 a = 3.99cm x sin x 9 x x sin Area of a triangle = x 36° 5 9 5 Area of a triangle = a b sin θ Area of a triangle =

  10. 2 Area = 8352cm Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager c PLT Skills AREA OF A TRIANGLE a b sin θ Area of a triangle = A TASK 3 (GRADE A*) 2 2 2 56 - 45 28 + = a c sin θ Area of a triangle = cos θ θ x 2 45 x 56 1) Find the missing lengths in the triangles below giving your answers to 3 s.f. : 10m 9m 4377 x sin 29.72 x 45 x (a) 56 Area of a triangle = (b) (c) 5040 4377 = θ B 5040 C Area of a triangle = 18m = 29.72° θ 2 Area = 864cm C a b sin θ Area of a triangle = 2 2 2 11 - 7 15 + = 45cm b c sin θ Area of a triangle = cos θ 28cm x 2 7 x 11 (f) (e) (d) -55 b² + c² - a² a² + c² - b² b² + c² - a² a² + b² - c² x sin 110.92 x 7 x 11 Area of a triangle = cos A = cos A = cos B = cos C = 154 θ 2ab 2bc 2bc 2ac -55 B = A θ 154 Area of a triangle = 56cm = 110.92° θ = = = = 2 2 2 2 cos cos cos cos θ θ θ θ 1 1 1 1 1 1 1 1 1 1 1 1 1 27.3m 36.0cm 65.0cm 625cm 2 2 2 2 2 2 2 2 2 2 2 2 2 a b sin θ Area of a triangle = - 1 - 1 - 1 - 1 cos cos cos cos 2 2 2 10 - 20 14 + = b c sin θ Area of a triangle = cos θ x 2 20 x 10 B C 304 x sin 40.54 x a 20 x 10 Area of a triangle = 5cm 400 304 = C 15cm θ 2 400 36° Area of a triangle = 7cm C A = 40.54° θ b 9cm θ a b sin θ Area of a triangle = a b sin θ Area of a triangle = B A 11cm 2 2 2 10 - 9 18 + = b c sin θ Area of a triangle = cos θ x 2 9 x 10 -143 x sin 142.60 x 9 x 10 Area of a triangle = 180 -143 = θ 180 Area of a triangle = = 142.60° θ

  11. 2 Area = 8352cm Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager c PLT Skills AREA OF A TRIANGLE A EXTENSION (GRADE A*) θ 1) Calculate the area of triangle PQR without a calculator: 10m 6m Q It does not matter which side given you take to be a or b a 6cm B C 18m 45° P Area = 8632cm 2 R Area = 864cm b 7√2cm C a b sin θ Area of a triangle = 45cm 28cm x x 7√2 sin 45 x 6 Area of a triangle = sin θ a b Area of a triangle = x x 7√2 θ x 6 Area of a triangle = B A x x sin Area of a triangle = x 5 9 56cm 42√2 √2 Area of a triangle = 2 √2 1 1 1 1 1 1 21cm 4 2 2 2 2 2 2 2 42 x 2 Area of a triangle = Area of a triangle = 4 B C a 5cm C 15cm 2 36° 7cm C A b 9cm θ a b sin θ Area of a triangle = B A 11cm

  12. It does not matter which side given you take to be a or b 2 Area = 8352cm Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager c Q PLT Skills AREA OF A TRIANGLE A a EXTENSION (GRADE A*) θ 2) Calculate the area of the kite below : 45° 10m 6m b P a b sin θ Area of a triangle = R b 7√2cm 25cm b c sin θ Area of a triangle = B C 18m a θ x sin 133.43 x 25 x 40 Area of a triangle = Area = 8632cm 2 60cm Area = 864cm Area of a triangle = C 40cm Area of kite = c 45cm 28cm Use the cosine rule to find θ b² + c² - a² Splits into two congruent triangles sin θ a b Area of a triangle = cos A = θ 2bc 2 2 2 40 - 25 60 + B A = cos θ x Area of a triangle = 5 x Cannot use the formula until we calculate a missing angle for θ 2 25 x 40 56cm -1375 = 2 2 2 cos θ √2 1 1 1 1 1 1 1 1 1 726.21cm 21cm 363.1074cm 2000 2 2 2 2 2 2 2 2 2 2 -1375 = θ 2000 - 1 cos = 133.43° θ C a b sin θ Area of a triangle = a 5cm C 15cm 2 x 7√2 x sin 45 x 6 Area of a triangle = 36° 7cm C A b 9cm θ x 7√2 x x 6 Area of a triangle = a b sin θ Area of a triangle = B A x sin x 9 11cm 42√2 √2 Area of a triangle = 4 42 x 2 Area of a triangle = Area of a triangle = 4

  13. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills AREA OF A TRIANGLE MINI-PLENARY – SPOT THE MISTAKES 2) 1) Find the length of c Find the area of the triangle sin θ a c sin θ a c Area of a triangle = Area of a triangle = 800cm x c 16 x 32 x sin = x 84 x Area of a triangle = x 67° sin 8 11 x c x = 8 sin 32 84 2 1 1 1 1 40.5cm sin ÷ Area of a triangle = 2 2 2 2 c x = 8 x cos 32 84 c = 19.8cm

  14. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager • LINK BACK TO OBJECTIVES • Accurately finding the area of a triangle using sine. What grade are we working at? DISCOVERY PLT Skills

  15. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills AREA OF A TRIANGLE PLENARY ACTIVITY– ASSESSING UNDERSTANDING (GRADE A) Applying the skills and knowledge you have acquired today, work out the area of the shape below: a b sin θ Area of a triangle A = x Area of a triangle A = x sin x 60° 9 13 D Area of a triangle A = B 7m a d sin θ Area of a triangle B = 85° C x Area of a triangle B = x sin x 85° 7 13 A 60° Area of a triangle B = 13m 9m Area of full shape = 50.7 + 45.3 2 2 1 1 1 1 45.3m 50.7m 2 2 2 2 Work out the area of each triangle and add the answers together Area of full shape = 96 B A 2 m

  16. What grade are we working at? Where are we in our journey? What have you learnt? Draw your brain In your brain, write or draw everything you can remember about finding the area of a triangle using sine. It can be a skill or a reflection, or something else that might be prominent in your brain.

  17. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? Plenary Activity How well do you understand the task? . I fully understand I don’t understand I nearly understand www.mistrymaths.co.uk

  18. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? Plenary Activity WWW (What Went Well) EBI (Even Better If) On your post it notes… Think about how you can improve your work. www.mistrymaths.co.uk

More Related