Question

please type out and show work. Thanks

LAW OF SINES 1. Marco drew a map of his hometown and wants to determine the shortest way to get from City Hall, where he works, to the school to pick up his children. He has made note on the first map of all the measurements known: the distance from City Hall to the First Bridge and various angles. Use the map to determine if the shortest distance would be to go toward the Bank, pass over the Second Bridge then head to school OR if the shortest route would be to take the First Bridge towards the Fire Hall and onto the school from there. ROADS --LINES OF GMT City will SELONO BRIDGE BENDEN RIVER Fine LAW OF COSINES 2. Prove that in triangle ABC, a = b cos C + c cos B. To do this, use the law of cosines or other cosine formulas to put different equations together Somewhat similar to how we go about solving systems by plugging one equation into another. (We will be doing a lot of this next chapter in trying to use different rules to help turn equations into something else that is helpful so I'm just trying to get you in that frame of mind!)

Answer 1

ANSWER

in AveD), 1.09 sin 55 spe singo OD sinq5' DE: 1:31m OD= 0.94m; sino, pentagon is formed So, nty+ 450 = 540 uty = 540-450 aty=90 It means , ABOD is right triangle (40=90) By pythagoras BO²+0D²= BD² 1.572 +0-942-B102 3944 fraggone 4:46 49+0.8836 = BD2 3.3485-BD2 BD-13.3485 BO=/(1183) Path BD = 1.83 mi) o distance - ACT CF +FE = 1.69 +1 +43 +1.51 = 14.63 mi)

palh ②, AB + B D T DE =0.86+1.83+1-31 2. So, path & path from is shortest of 4mi, that is fire mall to school. Law of cocines, Given & DABC Conctructiont Altitude AD Proof in AADC, Cosc = AG - – – I AC COSC = 46=4 > 100 = 6 COSC] -0. in D ADB, COSB = DB > {DB=CCOSB since, BC = BDTDC=a a = 66056 +C COSB from 0 & ® ] Hence Proved.