Question

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.

Answer 1

First draw a triangle, approximately right-angled.
Name the near-right-angle C (=85°20')
Name the opposite side (near hypotenuse) c.
Name one of the other sides a, and the opposite angle A. Name the remaining side and angle b and B.

Apply the sine rule:
sin A /a= sin C /c
Solve for angle A (approx. 44.2°)

Find angle B=180-A-C

Find side b, again using the sine rule:
b/sin B = c/sin C
from which b=38.7 approx.

or use the cosine rule:
b²=a²+c²-2ac cos(B)

Check your calculations using the cosine rule on the other sides/angles.