Known triangle ABC solution triangle. Angle a = 45 degrees, angle B = 75 degrees, B = 8, Angle a equals 60 degrees, angle B equals 45 degrees, a = 3.

Known triangle ABC solution triangle. Angle a = 45 degrees, angle B = 75 degrees, B = 8, Angle a equals 60 degrees, angle B equals 45 degrees, a = 3.

From the sine theorem
a/sinA=b/sinB
Substituting data
A = - 8 + 8 radical 3
C=180-B-A=180-45-75=60
Similarly, C = 12 radical 2-4 radical 6

In △ ABC, if a = 75 °, B = 45 ° and C = 3, then the length of the smallest side of the triangle is______ ．

∵ in △ ABC, a = 75 °, B = 45 °, C = 180 ° - A-B = 60 °, we can get that B is the minimum internal angle, so B is the minimum edge of the triangle. According to the sine theorem bsinb = csinc, we can get bsin45 ° = 3sin60 °; B = 3sin45 ° sin60 ° = 6, so the answer is: 6

In the triangle ABC, the side lengths of angles a, B and C are respectively a, B and C. It is known that a equals 75 degrees, B equals 45 degrees and B equals 4. Find the length of C

C=180-(A+B)=60
b/sinB=c/sinC
c=sinC*b/sinB
=√3/2 * 4/√2/2
=2√6

In the triangle ABC, we know that a = 75 degrees. B = 45 degrees. C = 3 and sign 2. Find A.B

Analysis
Because a = 75, B = 45
So C = 60
According to the sine theorem
b/sinB=c/sinC
So B / √ 2 / 2 = 3 √ 2 / √ 3 / 2
b=4√3
According to the cosine theorem
cosB=(a²+c²-b²)/2ac=1/2
(a²+18-48)/6√2a=1/2
Solution a = √ 138 / 2

In the triangle ABC, the following conditions are known: for triangle 1, a = 16, B = 16, 3, a = 30 degree; for triangle 2, C = 10, a = 45 degree, B = 30 degree

A / Sina = B / SINB,
16 / sin30 degree = 16 radical 3 / SINB,
SINB = root 3 / 2,
Angle B = 60 degrees,
So angle a = 90 degrees,
c^2=a^2+b^2
=256+768
=1024,
c=32.
2. Angle c = 180 degrees -- 45 degrees -- 30 degrees = 105 degrees,
Sin105 degrees = sin (45 degrees + 60 degrees)
=Sin 45 degrees cos 60 degrees + cos 45 degrees sin 60 degrees
=(radical 2 + radical 6) / 4,
c/sinC=b/sinB,
B = (csinb) / sinc = 20 / (radical 2 + radical 6) = 5 (radical 6 -- radical 2)
A = (csina) / sinc = (20 radical 2) / (radical 2 + radical 6) = 10 (radical 3 -- 1)

It is known that in △ ABC, ∠ a = 45 °, a = 2, C = 6

According to the sine theorem, Sin & nbsp; C = 62sin & nbsp; 45 ° = 62.22 = 32 (3 points) ∵ a = 2, C = 6, ∵ C > A There are two solutions to this problem, i.e. C = 60 ° or C = 120 ° (6 points) 1) when ∠ C = 60 °, B = 180 ° - 60 ° - 45 ° = 75 °, B = 3 + from b = asinasinasin & nbsp; B

In the triangle ABC, a = 2A = 30 degrees and B = 45 degrees are known to solve the triangle

a/sinA=b/sinB
2/(1/2)=b/(√2/2)
So ① B = 2 √ 2
②C=180°-30°-45°=105°
c/sinC=a/sinA
c/sin105°=2/(1/2)=4
③c=4sin105°=√6+√2

In triangle ABC, a = 45 degrees, C = 120 degrees, C = 10, solve triangle ABC

Sine theorem, a / Sina = B / SINB = C / sinc, just take the number in

As shown in the figure, in the triangle ABC, ab = 4, angle B = 30 degrees, angle c = 45 degrees, then BC=
It's a normal triangle sudu

Method 1
Pass a as ad ⊥ BC to d
∵ in RT △ abd, ∠ B = 30 °, ∠ ADB = 90 °, ab = 4, ∵ ad = AB / 2 = 2, BD = √ 3aD = 2 √ 3
∵ in RT △ ACD, ∠ C = 45 °, ∠ ADC = 90 °, ∵ CD = ad = 2
∴BC＝CD＋BD＝2＋2√3.
Method 2
According to the theorem of the sum of internal angles of triangles, it is shown that ∠ a = 180 °～ B ～ C = 180 ° - 30 ° - 45 ° = 105 °
According to the sine theorem, BC / Sina = AB / sinc,
∴BC＝ABsinA/sinC＝4sin105°/sin45°＝4sin（60°＋45°）/sin45°
＝4（sin60°cos45°＋cos60°sin45°）/sin45°＝4（sin60°＋cos60°）＝4×（√3/2＋1/2）＝2＋2√3.

In △ ABC, B = 45 °, C = 60 ° and C = 1, then the length of the shortest side is ()
A. 63B. 62C. 12D. 32

A = 75 ° can be obtained from b = 45 ° and C = 60 ° with the smallest ∵ B angle and the shortest edge B. from csinc = bsinb, B = csinbsinc = sin45 ° sin60 ° 63, so a is selected