one
1.5:3
2. Root number 3/3
3.2 Root number 2
4. Root number 3/4
5 From the sine theorem, we can draw the following conclusions:
a=2RsinA，b=2RsinB
acosA = bcosB
∴sinAcosA=sinBcosB
A and b are complementary.
∴C=90
Triangle ABC is a right triangle.
6.∵a/sinA=c/sinc
∴2/ (root number 2/2) = the square root of 6 /sinC
∴sinC= root number 3/2
∴∠ C = 60 or 120
∴∠ b = 75 or 15.
two
1. (root number 3+ 1)/4
2.60 or 120
3.30 150
isosceles
5. 100 meter
6. I didn't do this problem, I guessed it temporarily.
7.∫a/sinA = b/sinB = c/sinC
∴tanA=tanB=TANC
∴A=B=C=60
This is an isosceles triangle.
8.∵a/sinA=b/sinB=c/sinC=2R
∴R= 1
∴a=2sinA,b=2sinB,c=2sinC
∴ Original formula = [2 (sina+sinb+sinc)]/(sina+sinb+sinc)
=2
three
1.60
2.-2 Root number 3
3 Sina = a/2r，sinb = b/2r，sinc = c/2r，cosc = (a？ +b？ -c？ )/2ab
(A, B and C are the opposite sides of A, B and C respectively, and R is the radius of the circumscribed circle of the triangle)
A/2r=b/2r *(a？ +b？ -c？ )/2ab - ①
(a/2r)？ =(b/2r)？ +(c/2r)？ - ②
B = C； is obtained from ① simplification; Simplify from ② to get a? =b？ +c？
So the triangle is an isosceles right triangle.
4. Solution: (i) SINB =12/13 from COSB =-5/13,
From cosC=4/5, SINC = 3/5.
So sinA=sin(B+C)=33/65.
(2) 1/2*AB*ACsinA=33/2 by S△ABC=33/2,
∴AB*AC=65
∫AC =(AB * sinB)/sinC = 20/ 13AB
∴AB= 13/2
∴BC= 1 1/2
cosine theorem
one
1. Root number 7
2. 120
3.60
4. 1: root number 3: 2
5. From the meaning of the question, B is the biggest.
∵cosb=(a^2+c^2-b^2)/2ac= 1/8
∴ is an acute triangle.
6.∵cosB=(a^2+c^2-b^2)/2ac
∴c^2-8c+ 15=0
C = 3 or 5
∴S△ABC=6 root number 3 or 10 root number 3
two
1.60
2.6 root number 3
3.- 1/7
4. 120
5.45
6. 1
7. Let the angle added by two sides with side lengths of X and Y be 60 degrees. On the other side is Z.
1/2 * sin 60 * xy = 10√3->； xy=40
x+y+z=20
z^2=x^2+y^2-2cos60xy
z^2=(20-x-y)^2=400+x^2+y^2-40x-40y+2xy
0=400-40x-40y+3xy
x+y= 13
z=7
X=5，Y=8
8. make BC=a
In triangle ABC
cosB=(AB^2+a^2-AC^2)/2a*AB
=(a^2-33)/8a
In triangle ABD
cosB=(AB^2+BD^2-AD^2)/(2*AB*BD)
BD=BC/2=a/2
cosB=( 15/4+a^2/4)/4a
(a^2-33)/8a=( 15/4+a^2/4)/4a
(a^2-33)/2= 15/4+a^2/4
2a^2-66= 15+a^2
a^2=8 1
BC=a=9
three
1.2
2. Root number 3/3
3.60 or 120
4.√3 Sinar = 2 Sinar
SinC=√3/2 because Sina ≠0.
Because of the acute triangle, c = 60 degrees.
S=0.5absinC=ab√3/4=3√2/2
ab=6
c^2=a^2+b^2-2abcosC
7=a^2+b^2-ab=a^2+b^2-6
a^2+b^2= 13=(a+b)^2-2ab=(a+b)^2- 12
(a+b)^2=25,a+b=5
Only these
E-mail is too annoying.