Один из углов ромба равен 120 сторона ромба ровна 9 см. найдите меньшую диагональ ромба ​

9 см

Объяснение:

1) Рассмотрим ΔАВО

∠А пополам делит биссектриса АС ⇒ ∠ВАС = ∠А : 2 и ∠ВАС = ∠САD

∠ВАС = 120 : 2 = 60°

∠АОB = 90° (т.к. в ромбе биссектрисы перпендикулярны)

и чтобы найти ∠АВО = 180°- ∠ВОА - ∠ВАО (по теореме о сумме углов треугольника)

∠АВО = 180° - 60° - 90° = 30°

2) Катет, лежащий против угла, величина которого равна 30°, равен половине гипотенузы. В ΔАВО, АВ - гипотенуза, равная 9 см, а АО - катет, лежащий против угла 30°. Следовательно, АО = 9:2 = 4,5 см

3) Ромб является параллелограммом, а мы знаем, что в параллелограмме, диагонали точкой пересечения делятся пополам ⇒ АС = АО + ОС и АО = ОС = 4,5

АС = 4,5 + 4,5 = 9 см

Speaking Task 1. Choose the question from the card on the topic Entertainment and fedia^ prime prime and be ready to answer it after the teacher starts the conversation. Produce a speech by giving extended answers to the questions. Share your ideas with the class. Teacher organizes a Socratic seminar, which helps him/her to assess learners while they are speaking on the toplic Entertainment and Media and he/she prepares and cuts down questions and expressions beforehand. Learners sit in a circle and answer the question using in their speech some formal and Informal expressions to present logically connected information to their classmates. Expressions: Stating an opinion The way I see it... Sorry to interrupt, but... Is it okay if I jump in for a second? Can I add something here? Can I throw my two cents in? Not necessarily Interrupting If I might add something..... I beg to differ No, I'm not so sure about that That's for sure Expressing disagreement I'd say the exact opposite I have to side with somebody (name)on this one I was just going to say that In my opinion Expressing agreement If you ask me.. That's exactly how I feel As far as I'm concerned. If you want my honest opinion..... You have a point there That's not always the case​

2)

sinA =5,25/14 (геом определение синуса)

x/sinA =2*8 (т синусов) => x =16*5,25/14 =6  

3)

x+3 =y+2 (описанный ч-к) => y-x=1

Диагональ по т косинусов; cos120= -0,5; cos60=0,5

x^2 +y^2 +xy =9 +4 -2*3*2*0,5 =7

(x-y)^2 =7 -3xy => 1 =7 -3xy => xy=2

(x+y)^2 =7 +xy =9 => x+y=3

4)

sinB =sin(45+30) =√2/2 *√3/2 + √2/2 *1/2 =(√6 +√2)/4

2/sin45 =AC/sinB (т синусов) => AC =2√2(√6 +√2)/4 =√3 +1

√k +1 =√3 +1 => k=3

 

5)

AB=a, AD=b

P =2(a+b) => a+b =9

S =ab sinA => ab =20

a^2 +b^2 =(a+b)^2 -2ab =81-40 =41

cosA = −√(1-sinA^2) = −3/5 (тупой угол)

BD^2 =a^2 +b^2 -2ab*cosA (т косинусов) =41 +40*3/5 =65