We have an isosceles triangle;
A=opposite angle side a.
B=opposite angle side b.
C=opposite angle side c.
A=B
Method 1:
We can divide the isosceles triangle in two right triangles,
hypotenuse=7
side=9/2=4.5
B=A=arccossine (4.5/7)=49.994799...º≈50º
C/2=90º-50º=40º ⇒ C=2*40º=80º
Answer:
a=7; A=50º
b=7; B=50º
<span>c=9; C=80º
Method 2:
Law of cosines:
a²=b²+c²-2bcCosA ⇒CosA=(a²-b²-c²)/(-2bc)
CosA=(49-49-81) / (-126)=0.642857
A=arco cos (81/126)≈50º
B=A=50º
A+B+C=180º
50º+50º+C=180º
C=180º-100º
C=80º
Answer:
</span>a=7; A=50º
b=7; B=50º
<span>c=9; C=80º</span>
Solution:
The probability of an event is expressed as

In a pack of 52 cards, we have

Thus, we have the probability to be evaluated as
a)
there are total 3 diffrent shades
because
(i) A = C = 1/2 so one shade
(ii) B=D =F = 2/3 so one shade
(iii) E = 5/8 one shade
so total 3 different shade
b )
(i) y = 1/2 b
(ii) y = (2/3) b
(iii) y = 5/8 b