use the given information to solve the triangle.
C= 85 degrees 20'
a = 35
c = 50
I know that I have to find A,B,b but I do not know how to do this.
A=44degrees,14',28"
B=50degrees,25'32"
b=38.66
Use the law of sines first
sin C/c = sin A/a
that gives you A
then B = 180 - A - C
then use
sin B/b =sin A/a
85 degrees 20' = 85.33
Given a=35 and c=50
35sin85.33 = 50sinA
Sin A= 0.6977
A=44.24
B= 180 - 85.33 - 44.24
B= 50.43
50/sin85.33 = b/sin50.43
b=38.67
To solve the triangle, we can use the Law of Sines and the Law of Cosines.
First, let's find angle A.
We have angle C = 85 degrees 20'. To find angle A, we can use the fact that the sum of angles in a triangle is 180 degrees. So, angle A = 180 - (angle B + angle C).
Angle B is not given, but we can find it using the fact that the sum of angles in a triangle is 180 degrees. Thus, angle B = 180 - (angle A + angle C).
Now, we can use the Law of Sines to find side b. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is the same for all three sides.
So we have:
b / sin(B) = c / sin(C)
Substituting the given values, we have:
b / sin(B) = 50 / sin(85 degrees 20')
To solve for b, we can rearrange the equation and solve for sin(B) first:
sin(B) = (b / 50) * sin(85 degrees 20')
Now, using the inverse sine function (sin^(-1)), we can find angle B.
Next, using the Law of Cosines, we can find side a:
a^2 = b^2 + c^2 - 2bc * cos(A)
Substituting the values we have found, we can solve for a.
So, to summarize the steps:
1. Find angle B using the sum of angles in a triangle.
2. Use the Law of Sines to find sin(B).
3. Use the inverse sine function to find angle B.
4. Use the Law of Cosines to find side a.
Remember to convert all angles to the same units before making calculations.