5 Write a word from the box in each gap. fact.grow • lick • lifetime memory sweet
Horses are amazing animals! They have a great (1)
and they can remember people,
places and things that happen to them during their whole (2)
. They are quite
friendly too. They aren't often scared of people and they can (3)
food from a person's
hand while they stand in front of them. They are very (4) ►
animals when they are
young. They really like to play! They (5)
quite fast and they become adults after
about four or five years. An interesting (6)
is that horses only sleep for about three
hours a day, and they usually sleep while they are standing. Imagine people doing that! No need
for beds!​

ΔАВС- равнобедренный.Пусть  АВ=ВС =а. ВЕ⊥ АС=10 см, DC⊥АВ=12 см. Найти R окр.,описанной около Δ СDB.
ΔCDB - прямоугольный. R=1/2·BC.(Радиус окружности ,описанной около прямоугольного треугольника = половине гипотенузы)
S(ΔDBC)/S(ΔABC) = DB·BC/AB·BC   ⇒  S(ΔDBC)/S(ΔABC) = DB/BC (1)
S(ΔDBC)=1/2 DB·DC=1/2·DB·12=6·DB                S(ΔDBC) = 6·DB
S(ΔABC)=1/2 AC·BE =1/2AC·10= 5·AC                 S(ΔABC)=5·AC
Получили,что S(ΔDBC)/ S(ΔABC) = 6·DB /5·AC  (2)
Следовательно, DB / BC = 6·DB / 5·AC      ⇒ 5AC=6BC  (3)
Из  Δ ВЕС  найдём  ЕС =х по т. Пифагора : ЕС²=ВС²-ВЕ²
х²=а²-10² ⇒ х=√а²-100     АС=2х=2·√а²-100
Используем (3) равенство :  5 АС=6 ВС и  АС=2х   ⇒
5·2√а²-100 = 6а  ⇒  100·(а²-100)=36 а²  ⇒  64 а²=10000  
а²=10000 / 64   ⇒  а=100 / 8    R = 1/2 a   =  50/8 = 25 / 4

Объяснение:

∠C=60∘; AC = \sqrt{2} + \sqrt{6}AC=2+6 ; BC = 2\sqrt{2}BC=22 .

Объяснение:

1) Найдём \angle C∠C :

Сумма внутренних углов треугольника равна {180}^{\circ}180∘ .

\Rightarrow \angle C = {180}^{\circ} - (\angle A + \angle B) = {180}^{\circ} - ({45}^{\circ} + {75}^{\circ}) = {60}^{\circ}⇒∠C=180∘−(∠A+∠B)=180∘−(45∘+75∘)=60∘

2) Найдём BCBC :

По теореме синусов: \dfrac{AB}{\sin(C)} = \dfrac{BC}{\sin(A)}sin(C)AB=sin(A)BC

\Rightarrow BC = \dfrac{AB \cdot \sin(A)}{\sin(C)} = \dfrac{2\sqrt{3} \cdot \sin({45}^{\circ})}{\sin({60}^{\circ})} = \dfrac{2\sqrt{3}\cdot \dfrac{\sqrt{2} }{2} }{\dfrac{\sqrt{3} }{2} }=\sqrt{3} \cdot\sqrt{2}\cdot \dfrac{2}{\sqrt{3} } = 2\sqrt{2}⇒BC=sin(C)AB⋅sin(A)=sin(60∘)23⋅sin(45∘)=2323⋅22=3⋅2⋅32=22

3) Найдём ACAC :

Пусть xx - AC.AC.

По теореме косинусов:

AB = \sqrt{{BC}^{2} + {AC}^{2} - 2 \cdot BC \cdot AC \cdot \cos(C)}AB=BC2+AC2−2⋅BC⋅AC⋅cos(C)

(2\sqrt{3})^{2} = (2\sqrt{2})^{2} + x^{2} - 2 \cdot (2\sqrt{2}) \cdot x \cdot cos(60^{\circ})(23)2=(22)2+x2−2⋅(22)⋅x⋅cos(60∘)

\begin{gathered}12 = 8 + x^{2} - (2\sqrt{2})x\\12 - 8 - x^{2} +( 2\sqrt{2}) x = 0\\-x^{2} + (2\sqrt{2}) x +4 = 0\\x^{2} - (2\sqrt{2}) x - 4 = 0\end{gathered}12=8+x2−(22)x12−8−x2+(22)x=0−x2+(22)x+4=0x2−(22)x−4=0

\begin{gathered}\\x = \dfrac{-(-2\sqrt{2})\pm\sqrt{(-2\sqrt{2})^{2}-4\cdot1\cdot(-4) } }{2\cdot1}\end{gathered}x=2⋅1−(−22)±(−22)2−4⋅1⋅(−4)

\begin{gathered}x = \dfrac{2\sqrt{2}\pm\sqrt{8 + 16} }{2} \\x = \dfrac{2\sqrt{2} \pm2\sqrt{6} }{2} \\ x_{1} = \sqrt{2} + \sqrt{6} \\x_{2} = \sqrt{2 } - \sqrt{6}\end{gathered}x=222