SOLUTION: A= 25 degrees a=5 b=11 Solve the triangle ABC Thank you!!

Algebra.Com
Question 1151811: A= 25 degrees
a=5
b=11
Solve the triangle ABC
Thank you!!
Found 2 solutions by ankor@dixie-net.com, jim_thompson5910:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
A= 25 degrees
a=5
b=11
Solve the triangle ABC
Use the law of sine to find angle B: = =
=
cross multiply
5*sin(B) = sin(25)*11
5*sin(B) = 4.6488
sin(B) =
B = 68.40 degrees
:
Find C:
180 - 25 - 64.4 = 86.6 degrees
:
Find c
=
c = sin(86.6)*11.83
c = 11.81 the length of side c
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Angles
A = 25
B = unknown
C = unknown

Sides
a = 5
b = 11
c = unknown

We have two known sides an angle that is not between the two sides. This is the SSA case which has 3 possibilitiesThe SSA case leads to ambiguity.

Use the law of sines to solve for angle B
sin(A)/a = sin(B)/b
sin(25)/5 = sin(B)/11
0.0845236523481399 = sin(B)/11
11*0.0845236523481399 = 11*sin(B)/11
0.929760175829539 = sin(B)
sin(B) = 0.929760175829539
arcsin(sin(B)) = arcsin(0.929760175829539)
B = arcsin(0.929760175829539) or B = 180 - arcsin(0.929760175829539)
B = 68.3974616057519 or B = 111.602538394248
B = 68.397 or B = 111.603

If B = 68.397, then C = 180-A-B = 180-25-68.397 = 86.603
If B = 111.603, then C = 180-A-B = 180-25-111.603 = 43.397
In either case, the value of B produces a positive C value. Therefore, we have two sets of solutions to represent the two possible triangles.

With this info: C = 86.603, a = 5, b = 11, we can find the unknown side c using the law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = (5)^2 + (11)^2 - 2*(5)*(11)*cos(86.603)
c^2 = 25 + 121 - 110*0.0592541057795245
c^2 = 25 + 121 - 6.51795163574769
c^2 = 139.482048364252
c = sqrt(139.482048364252)
c = 11.8102518332274
c = 11.810

So one solution consists of
Angles
A = 25
B = 68.397
C = 86.603
Sides
a = 5
b = 11
c = 11.810

--------------------------------------------------

Use the law of cosines again, but now with C = 43.397
The values of 'a' and b stay the same
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = (5)^2 + (11)^2 - 2*(5)*(11)*cos(43.397)
c^2 = 25 + 121 - 110*0.726610645792925
c^2 = 25 + 121 - 79.9271710372218
c^2 = 66.0728289627782
c = sqrt(66.0728289627782)
c = 8.12851948160169
c = 8.129

The other solution consists of
Angles
A = 25
B = 111.603
C = 43.397
Sides
a = 5
b = 11
c = 8.129


--------------------------------------------------


In summary, the two possible triangles are
Triangle #1Triangle #2
Angles
A = 25
B = 68.397
C = 86.603		Sides
a = 5
b = 11
c = 11.810		Angles
A = 25
B = 111.603
C = 43.397		Sides
a = 5
b = 11
c = 8.129


Diagram

The decimal values are approximate to three decimal places.
RELATED QUESTIONS

How do I solve the triangle ABC when A=35.8 degrees and c = 6.9mm? Thank... (answered by Alan3354)
Given that A= 25(degrees), B=43(degrees), and c=17, solve triangle ABC. Round to the... (answered by Alan3354)
Solve triangle ABC where A = 25 degrees, a = 9cm, and c = 11cm. Include the ambiguous... (answered by Alan3354,MathLover1)
Consider a triangle ABC. Suppose that a=25, b=28, and c=5. Solve the triangle. Carry... (answered by Alan3354)
The perimeter of a triangle ABC is 500m. A=40 degrees and B= 60 degrees. Find the... (answered by cleomenius)
Q. In a triangle ABC, angle B= 55° and angle C=65°. Is the triangle ABC isosceles?... (answered by josgarithmetic)
In triangle ABC, b=11, c=18, and angle B=40 degrees. solve the... (answered by venugopalramana)
Solve triangle ABC using the given measurements. a.B=50 degrees, a=18 b. A=33 degrees,... (answered by Fombitz)
Determine the solutions of triangle ABC if: Angle A=39 degrees Side b=10 cm Side... (answered by Alan3354)