Math GCSE ; trigonometry, pythagoras and angles

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190 I DO Wark cul the size of angle ABC. You must show all your working and increase give ressons for your answers. 1710 YOU DO Work out the sizes of the angles marked with letters. y: 40° 0 x= 140° 2 D y: 20 .6x₁ 1:30 X=46 5 a b C d. e ♡ 551 X 0.95 6000 6000 x 1.7 original change Y = 40° x= 60° 3 1.241 X = 130⁰ 6 λ monday Angle A = 523.48 £580 O.V = d^ in price = 2440 x £6354 9225.6. angle d 2 Y = 100* X=20* Co 2431012 new 28th November 2022 properties interior angle x + y = 180 angie y = 35 +68 = 103° 2 :120 : x 100 2 angle b + c 3 a YOU DO APurposeful practice 1 Calculate the size of one interior angle of a regular polygon with 2.16 sides 5 19 sides 418 vides Where necessary give your answers to 1 dp Purposeful practice 2 Calculate the size of the missing angle in each irregular polygon 2 D C far APurposeful practice 3 Find the number of sides for each polygon 1 Polygue with sum of interior angles of 720 2 Polygon with sum of interior angles al 1600 3 Pulygn with sum of oranges of 3960" The diagram shows a regular octagon and a regular hexagon, Calculate the size of the angle a. You must show all your working x=110 185° 95° 66° tye 0 y 400 n THE TW 105⁰ Exteniar angles in a polygon. S x+y = 180° 110° P140⁰ Exterior angle 40 = 360 = TP 140⁰ 99⁰ x=120° 6 12 360 9 24 Sum of exterior angles are 360° of a polygon Each interior angle of a regular polygon is How many sides dores it hve? - -40% Droe 3 17 sides +40 a. (n=2)x180 6:16=2 x 150 C. 17-2 x 180 x=157⁰ d. 18-2 X 180 *436° e-19-2x 180 = 360 n 180-95 85199 + 110 = 294 360 294 = 66° I Do Work out the size of each unknown interior angle in these irregular polygons to find the size of one exterior angle to do you have the sum / number 360 20 5-2 3x180 - 540° 2r -6 Thursday (500, 150-130 салып 1100 60 = 2700 = 17- = 2850 - 18 - 3060 - 19 = 2022 130° 6x = 370. x=61.6 - 13x180 = 2340-15 = 2880 16 = 180° 1580 2x-50 80° d 1000 1st December a =6 180-120 120° 180-86 Exterior angles a polygo 25c 2x-50 2(616) x + 40 = 61.6 F40 = -30 660 b 120° ♡ 1x + 40° 2x + x + 2x-50+ x + 40 = 360 6x-10 = 360 tio = +10 2 (616) = 123.3° = 101.7 €190% 180-90 Example = 180° = 1610 73.30 d. e. 9 i a d. C c. 12m D 2m 2m 12m чсм h 6cm 5.9 넣히나 나의 6 Sc си п 3 1 62.41 5m 13m [ 6n 16 = 45 5cm with b C. = 360 73.3° 7 do 0 3cm 6cm 5cm a. 12cm 5.9 b. с 16cm. си п d. 62.41 2m e 2 2 C = atb Sm 12m Friday 2nd December. -2022. Puthanaras theorem. c² =q²tb² 169=144+25 √169=13 2m 3 = 3²+4² 9+ 16 = 25 C = 13cm find out if these are right angled c²=a² + b² 5cm 6² +5² = 61 0= 7.8 10cm 10² = 6² + x G 7.9cm □ 9.9cm 13m 7m this is right angled 13m 5m 82 c²₁² = a ²₁+ b² 9.9% = 7.9² + 5.9 ² x 6m This is not night angled Hviled c²=a² + b² 13² = 5² + 144 = 12²m calculate the Missing length ܐܘ ܐ 53= 2² +72 = 7.3²m 2 c² =0 tb 13²=12² +25 = 5²m 532 c² = a² + b² 6² = 2² +32 = 5.7²m 2 C = a + b 169 = 12² + 5² = 13² m 90° um O problem solving A ship sails 5 miles North and then 8.1. miles east. Then to starting point. what is the total distance travelled? X 15 New learning km b 8.9 n Sum of interior (n-2) x180 = 1440 cm 12m D c² = a² + b² PI park 2 1440 - all sides. = 335° C = hypoteņuse is. longest side is oppositi the right angle only works for right angle triangles x 8.1m A roof truss is made The vertical bisects horizontal of wood 5m | 258 720²-650² = x = 12 cm 10-2 *180 wood costs 17.50 per metre work out total cost? tall sides №m 4cm x 3cm 17.5cm c²= a² + b² C² = 5² + 8.1² 2 C = 9 52 6² +4² = 7.2² monday 5th December 2022 70° ܐܐ 2²²=2²+ b² 12 = 5² + 144=25 + 119 17.52 8.9² = 15.12 15.12 2 c²=a² + b² 4²-3²+52 2√7 substitute = 12²= 5² + 10.9² = 10.908... = 10.9 (1d.p) c²=XQ² + b² 17·5² = 8.9² + N 7.22 7 PRACTISE a. b. с d. ta 18/ b.x CIA 6 x 5 х 10 2.1 8= 2/8 xu 60° x A150 10 o 545 ио X2:1 =4 = 5x10 15 a = 3.5 ALO xh xu = 9.5 N 04cm 20° C-A B-C VINES x =16 x 201 x10 n x2.1 x = 50 x tane = 0 VERORDI find angle z a ON 2 x = 7.35 7 x = 95 x 105 cah eta COSI5° = 18 monday su 2022. x à 15 a 15x tane 40 = x alumn 2 XX xcos 15 = 18 cos150 -8cm H 160° 2 = 120° inverse of sine is sin t'e -Inverse of cos e is costie Pinverse of tane is tante x = 18/cos 15° x=18.6 Thursday ofth December -2022- x = 12.6 11-dp] 60 ✓ calculare size of 8 to 0.1° = tan@ 40% Xxx SOH Sing= 4 xsine Sin ¹0 sine == SinT 0 = 30° () Trodda Buipunjamwanadhy bound to brings um vos boisn stipr burn 8 KW x 27 30 adjacent (aner angle) SOH CAH TOA Sine = Opposite Cos-Adjacant 6 hypotenuse hypotenuse e 1 Do 5a a 260 36° 40 U H opposite b O H 10 35° a O 8H xnxx 15h = 22.8 apport each other hypotenuse X5 8 X Sine 35 = x x = 4.6 (Soh Cah toa Sine 35 x8 sin e n sin26 <=10 xsin26 = 10 x = 10 tan = cane = a h sin26 can x ²/² = (ah 36° 15 X15 15x can 36° = x x = 12.1 = 0 tan 62 x 5x5 tane = O 5x tane-x x = 9.4 (1-dp) a tan 27° = 4 xx xxx xtan27⁰ =4 tan 27 x = tan27/4 x = 7.9 opparite to = tan27 = of interest Fan= app 7x8 с b e adjale c C a 2.1 IN 12 SXI n 1⁄2 6. 2015 7SK h=i a 5x 7 12x =45 df 8x4= 1/2 x 102 C P 36 = 6 <= 1 b с 06 a I DO e 6cm દુ O 0 a e 9.5 cm O n 0 H 10cm n 04am O P 2² 4535 ½2 (10)× 4 8 = (05-~(-5) = 53/ 10 Cm SXK =30 n = 6cm COSO = 6 COS-1 10 angle P= 56.03⁰ POQ? tang = 6.4 tan 9.5 tan3397° = 6.4 x95 A.S xa.s 9.5x ton 33.970 = 6.4 tan - tan Homestudy (3+7)x==30 ½/2 (+9) x k 2(sxk us = US 7 SK h = u5 h = 60m✓ Thursday oath becember 2022. 0 = 33. 34 8 = 33.97 = 30 4 5x7=35 1/2x4x5=10 (3 =45cm²✓ d 8x9 = 72 1/2 x 15x5=367 102 cm² 36:4 = 90 p=gram a = 81cm? 1. 2. 3. 4 friday 16th December - 2022. 6₁ test feedback 1.dp 0 064 to 1225 = 0.0601 to 2 S.F = 1200 1.dp = 4.09 4.1 a. 4x7 2 4.09 to 22/01/23 challenge = 14cm²; 4 x 14 = 56cn 12756 14 = 28 = 4 1st ㅋ 2 K=4✓ (3)