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数学 高校生

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例題38 応用問題 (解答 sin 18°の値 二等辺三角形ABC の頂角 A の大きさを36° 底角Bの二等分線が 辺ACと交わる点をDとし, BC=2 とする。 これを用いて, sin 18° の値を求めよ。 考え方)図で,∠BAE=18, BE=1 であるから, AB がわかると, sin 18°の値が求められる。 △BCDS △ABC を利用。 △ABCにおいて,∠A=36°, ∠B=∠C であるから ∠B=∠C= 180°-36° 2 よって, △BCD において -=72°1 72° 2 2組の角がそれぞれ等しいから AABCOABCD 第1節 三角比 71 ∠DBC= =36°, ∠C=72° よって よって AB: BC=BC:CD また, ∠DAB=∠DBA=36° であるから, △DAB は DADB の二等辺三角形である。 △ABCS ABCD より BCD は BD = BCの二等辺三角形であるから DA=DB=CB=2 B x2-2x-4=0 よって, AB=x とおくと, CD=AC-AD=x-2であるから, ① より x:2=2: (x-2) x(x-2)=4 7 1 E ③8 242 例題 38 の図を利用して, cos36°の値を求めよ。 243 (1) 右の図において, BD の長さを求めよ。 203 (2) 右の図を利用して, sin 15℃, cos 15° の値を求めよ。 A B D すなわち x>0 であるから x=1+√5 したがって, Aから辺BCに垂線 AE を下ろすと, ∠BAE = 18° であるから BE 1 1 √5-1 sin18°= 4 BB===√5 +1=(√5 +1)(√5-1) 答 AB x 1 C 第4章 ヒント 243 (2) 点Dから辺ABに垂線DHを下ろすと, ADHは直角三角形でHAD=15° 図形と計量 A 60° 45° D 1 --'C

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英語 高校生

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Omoiyari is said to be a key concept of the Japanese mentality. (Its primary meaning is the ability to imagine other people's feelings. Japanese people's good manners have often (2) been associated with it and reported in news articles. For example, Japanese soccer supporters cleaned up the stadium after the matches at the World Cup, actions that were praised by the foreign media. Some experts say the supporters' behavior is related to education in Japan, where children clean their classrooms every day. Another example was seen during the frequent natural disasters. Even in such situations, many people still kept calm and patiently waited in lines for emergency supplies. JANET [ 3-1 ] According to a survey by an organization to promote good manners in Tokyo, less than 30 percent of Tokyo residents think people in Tokyo have good manners. [ 3-□ ] For example, Tokyo residents notice bad manners on the train. (4)Some young people sit in priority seats and do not give sit (5). V₂ 1 up their seats to the elderly, and others put on makeup. [ 3-> ] In an effort to get the passengers to 52 act more (5), railway companies display posters, saying things such as, "Please line up and c wait your turn" or "Please switch your phone to silent mode while ( 6-a) the train." 5 [ 3-= ] Omoiyari is often seen in school mottoes and emphasized in moral education at school. Some of the values that students are ( 6-b) include respecting the elderly, helping those with disabilities, and keeping promises. Students also take turns (6-c) in charge of cleaning the classroom, serving lunch, taking care of plants and animals. In addition, volunteer clubs collect money for charitable organizations and members visit elderly people in nursing homes. In moral education class, students read stories and discuss the topics in them. The teacher facilitates the discussion and the students draw their own conclusions. (Nakaya, et al., Discuss the Changing World, Seibido)

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