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数学 高校生

(1)cosの求め方を教えてください (2)正弦定理使えますか?

重要 例題 141 四面体上の折れ線の最小値 11 四面体 ABCD があり, AB=BC=CA=8, AD=7 である。 COS ∠CAD= のとき、次のものを求めよ。 14 (1) 辺 CD の長さ 000 (2) ∠ACD の大きさ 基本 121,137 (3) 辺 AC上の点Eに対して, BE+ED の最小値 CHART & THINKING (1) (2) 辺 CD, ∠ACD 空間の問題 平面図形 (三角形) を取り出す を含むのは ACD (1), (2) 求めるものを含む三角形はどれかを 見極めよう。 A (3) 空間のままでは考えにくい。 △ABCと △ACDを1つの平面上に広げ, 平面図形と して考えよう。 E ⇒ B< D PE B (3) 辺 AC の D C まわりに広げる C 解答 (1) ACD において, 余弦定理により CD2=7+82-2・7・8cos∠CAD=25 CD> 0 であるから CD=5 (2) ACD に余弦定理を適用して A ( COS∠CAD= 11 8. 8 S)xS D B 82+52-72 COS ∠ACD= 8 2.8.5 2 C よって ∠ACD=60° 14 E A 1 (3) 右の図のように,平面上の四角 ← 四面体 ABCD の側面 8 形ABCD について考える。 7 3点B, E, D が1つの直線上に あるとき, BE+ED は最小になる。 よって, BCD において, 余弦 定理により B △ABC, △ACD を平面 上に広げる。 1 E D 8 60°60° 最短経路は展開図で 2 120°- 50 点を結ぶ線分になる。 C BD2=82+52-2・8・5cos <BCD=129 BD> 0 であるから BD=√129 <+2BCD = ∠ACB + ∠ACD=120° したがって, 求める最小値は √129 1 cos 120°--- 2 NFORMATION 折れ線の長さの最小値 3)BE+ED は折れ線の長さと考えられる。この長さは, 折れ線がまっすぐに伸び して線分になるとき最小となる。 2点間の距離の最小値は, 2点を結ぶ線分の長さ ACTICE 141 ■の長さがαの正四面体 OABCにおいて,辺AB, BC, OC それぞれ点P,Q,Rをとる。 頂点から,P,Q,R の順 点を通り、頂点Aに至る最短経路の長さを求めよ。うら 0 A P Q 1 R 11

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数学 高校生

どうしてこれで等式になるのでしょうか、?

補充 例題 129 三角形に関する等式の証明 とき、 の二等分線と辺 めよ。 基本 120 121 △ABCにおいて,次の等式が成り立つことを証明せよ。 (1) asin Asin C+bsin BsinC=c(sin' A+sin*B) (2) a(bcos C-ccosB)=b-c CHART & SOLUTION (1) p.194 基本事項 1.2| 三角形の辺や角の等式 辺だけの関係に直す 利用して、(2)で に代入する。 等式の証明はか.178 INFORMATION の1~3の方法がある。 (1) はるの方法,(2)は1の方 法で証明しよう。 (1) 正弦定理から導かれる sinA= 2R など (Rは外接円の半径)を, 左辺と右辺それぞれ (2)余弦定理から導かれる cos C= a2+62-2 などを左辺に代入する。 2ab 解答 A (1)△ABC の外接円の半径をRとすると,正弦定理により asin Asin C+bsin Bsin C A:AE b 4R2 C AD // EC と したがって, 与えられた等式は成り立つ。 EC=∠BAD 別解 ACE から よって (左辺) =2Rsin' Asin C+2Rsin Bsin C =2R sin C(sin2A+sin2B) △ABCの外接円の半径をR とすると, 正弦定理により a=2RsinA, 6=2RsinB,c=2RsinC a c =a° 2R 2R 2R 2R ={(2R)²+(20 = c(a²+b²) c(sin'A+sin°B)={(2x) b C c(a2+62) 4R2 辺だけの関係に直す a sin A= 2R' b sin B= 2R' =c(sin'A+sin'B)=(右辺) sin C=T 2 を代入 2R inf. 別解では,角だ 関係に直してうまくし が、数学の範囲で b c を sinAなどの けの関係に直しても 後の変形の知識が不 B:AC

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英語 高校生

例文暗記について相談です 最近、例文暗記を進めていくごとにこれはaかtheか、 複数形か、thatはつけるのか省くのか、 という細かいところまでこだわっています。 時々、これが例文暗記の目的だったのだろうか? もっと色んな英作文ができるようになりたいし、 覚えた文を使っ... 続きを読む

3 ⑥64 n would be dangerous to drive a car after drindy a D every dangerous to two bottles of whiskey, E n e light turns green 9 ss a busy strest befol Some Japanese high school students 改訂新版 tis vary pleasant to take a walk early When waiting for the elevator to come or the traffic light rated within only thirty An elderly woman sitting Sam suggested that we a inconvenient. Everyone should be free It is impossible to Pred insisted p birds singing lis pare for university entrano su nge, most Japanese pe ドラゴン・ nt a car to and who to have ph イングリッシュ It never ocked Tom, dinner is r I'll give you a call when yout Thave This 基本英文100 100 Basic Sentences for Writing 駿台予備学校英語講師 学研プライムゼミ特任講師 I the host parents treated me just She The best thing about my stay with an Ar doughint 1 lived in C CD付き widely used years. 竹岡広信 father was transferred there. have been rapidly increasing Citr I have often heard him boast that he is very good at swimming, but i have never actually seen him swim. has been only a week since I began working part-time at a corverience store, but am already quite used to it. When I got on the train this moming. I could not find an empty seat. Fes not wearing my glasses now, so I can't make out what the sign says.. 「Even ten years after returning from living in France, I still find myself thinking in French. By the age of five or six, humans learn to express how they feel. Last year, I took two weeks oft, and went on a trip to Europe with my family. Bab had grown a beard, so when I saw him at a class reunion, I did not recognize him. - stayed up until four last night preparing for my math lesson, so feel very sleepy. The teacher says that we should wait here for a while because if we left now, we might get caught in a thunderstorm on the way down. People wish they could live forever and never get older. However, if this came true, there would be too many people on the Earth. Ann looks happy. Something good must've happened to her. Capt new amployee is too friendly Hot When I was a child, I often used to wish L Iwere his friend. KODANSHA use were a little larger. At tile to work as a volunteer helping victims of natural disasters, such as floods or earthome

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英語 高校生

黄色線のhis business が 干渉しないよう という意味になるんですか😵‍💫

3,000 animated characters. 2 Blanc was born on May 30, 1908, in San Francisco, California. However, when he was a child, his family moved to Portland, Oregon, where he attended 問1の正解の根拠 ~へ引っ越した 〜に通った school. When he was young, a game he used to play by himself was to look at, よくしたものだ 一人で for example, a bird, and try to imagine what it would sound like if it could talk. Then, he would try to make the voice that he had imagined. 問1の正解の根拠 ~を集めた 問1の正解の根拠 3 In 1927, Blanc began working for a daily radio program. There, because the sponsors could not afford to hire more actors, Blanc used his own voice for many of the show's characters. After that, he moved to Los Angeles, California, where he joined Leon Schlesinger Productions, an animation studio that had assembled some of the greatest voice actors of the time. This company did the work for Warner Brothers, which developed the cartoons that made Blanc rotair lo subiq soloqu na diw envoys abiyong liw 4 Without a doubt, Blanc's most famous voice is that of Bugs Bunny, the star of the Warner Brothers animated line-up since 1940. Blanc not only provided Bugs Bunny a voice, but also a personality and his famous catch-phrase, "What's up, doc?" The team involved in creating Bugs was very careful about famous. 〜に関わった 問3の正解の根拠 giving him a personality that would be popular for everyone. They decided that Bugs would not be an unkind character; he would just always be peacefully minding his business until someone started trying to hurt him or make him do something he did not want to do. Then, he would fight back. Blanc was very JAKE 問3の正解の根拠 proud of Bugs and thought that the character could be a role model. He said, "Bugs does what most people would like to do but don't have the guts to do." 問2の正解の根拠 5 By the 1940s, Blanc was providing the voices for more than 90 percent of the Warner Brothers cartoon characters. To put that in perspective, from 1940 to 1959, Warner Brothers released almost provided about 540 voices during that time. それを総体的に見ると 600 cartoons. That means Blanc Through this time Blanc appeared on many radio and television programs. He provided the voices for the most 問1の正解の根拠 lovable side characters on extremely popular programs of those days. Then, in the 1960s, he voiced some of the characters in "The Flintstones," the first -126- 生 H

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