Two angles of a triangle and the measure of the side opposite one of them are given. Find the measure of the side opposite the other given angle, but do not use a calculator.

Question

a = 4.6, α = 45°, β = 60°

(I only to know the solution on how to do it)

Answer 1

use the Law of sines

b/sin60 = 4.6/sin45

b=(sqr3)/2 times 4.6/sqr2/2

=4.6(sqr1.5) = exact answer

= about 5.633826408

3rd angle = 180-60-45= 75

a/sinA = b/sinB= c/sinC

4.6/sin45 = 4.6(sqr1.5)/sin60= c/sin75

c=4.6sin75/sin45

c>b>a

C>B>A