cosinerule余弦定理

1、LESSON P LAN FORMAT Course: Bilingual math | Grade Level: grade 2 Teacher:Bela| Date: Title: cosine rule Content: Trigonometry PRE-LESSON PLANNING Learning Objectives 1. Lear n to deduct the theorem of cos ine rule 2. Un dersta nd the meaning of cos ine rule 3. Be able to use cos ine rule to solve q

2、uesti on Design the Assessment Exercise p age 201 Design Assessment Rubriftf Needed) TEACHING THE LESSON Vocabulary: Materials: acute tria ngle obtuse tria ngle right-a ngle tria ngle perpendicular IGCSE MATHEMATICS BOOK p rocedure C 1. Review- Sine Rule The formula of Sine Rule? sM sin5 sinC sin/ _

3、 sinZJ _ sinC a b Exercise: 旳 AEIC AC 二 6则 BC-5cm andZA-120 Find ZB Solution: sin _ sin 4 b Q sin B _ sin 120* 6 15 .6其班11120 sm B = 14 B ia* 1418 sin30 sinZ# sinC b b B D C 15 sin B = 0.346 B= 20.27 Sometimes the sine rule is not eno ugh to solve the p roblems Like this. c 2. New knowledge Cosi ne

4、Rule In any tria ngle, a2 = b2+ c2 - 2bc cos A b2 = a2 + c2 - 2ac cos B c2 = a2 + b2 - 2ab cos C Proof : 1) In an acute triangle Draw the perpen dicular from A to meet CB at D. A a D From / ABD AD=?, BD=? From / ADC Aiy = ACAn(fiD=BCCD C7J = /CciC = ACsisiCf =AC sin，C+CJi -ICB ACC+AC cos C = AC+Clf

5、2CB ACim&C ：/二/ + 庐-2仍 cosC 2) In a obtuse tria ngle Draw the perpen dicular from A to meet CB at D. A + b? - 2(ib cos C ?= 3. Summary Cosi ne Rule c From / ADC AJ) = /C!iin(18r-C) = dCsiin C CO =tos(l(rCJ = -AC cosC From / ABD AS* 二加 +M = (CsinCy +(CB + CJ)f = AesiDC+CB-2CBACcosC+ACcosC 二店 + 前-2CB

6、McosC 二+2-2处 cosC 3) In a right-angle triangle. From Pythagorean theorem we can also get that cos5= lac 严/+几 cos C= 2ah Exercise In the acco mpany diagram, find BD to 2 decimal p laces. Solutio n： 加心笙 厶饬二IK(尸I巧0=45。 R厂in =,BC = 1 心MMi sin 85 sin 45 ZAtiC=3S-nS = 5Vr 19 一 =,7lC = 130()0 shi5 血4于 = A

7、= krtanl5 i/f 怙讣55 辭nd 600 tan 10 AA4tDJdCI7 ZiCD=135/C=13,0(HfO=悟 18? =13.000?+_/-2xl3xjxa*iB5 y+l8JS5v-l55=0 v-6283 r BD=BC+CD=16.906+6.283=23.189=23.19 App licati on p roblems A fishi ng boat leaves a harbour (H) and travels to East for 40 miles to a marker buoy (B). The n the boat turns left and

8、 sails for 24 miles to a lighthouse (L). It the n returns to harbour, a dista nee of 57 miles. a) Make a sketch of the journey. b) Find the bearing of the lighthouse from the harbour. (nearest degree) n L 57 miles/ - / / 24 miles Exercise A barge is moving at a con sta nt sp eed along a straight can

9、 al. The an gle of elevation of a bridge is 10. After 10 minutes the angle of elevation is 15. After how much Ion ger does the barge reach the bridge? Give your an swer to kC600 + f3tanl0 - L/f tanlS feOOtar W + f tanW =f tanlS Check for Student Understanding by: Guided P ractice Check for student understanding by: Some exercise Closing Activity Summarizing the Learning STUDENT WORK Inde pendent P ractice POST LESSON ACTIVITIES Student