Question

Viewed from earth two stars form an angle of 83.23 degrees. Star A is 33 light years from earth, and star B is 21 light years from earth. sketch a diagram modeling this situation and find out how many light years the stars are away from each other.

Answer 1

First, illustrate the problem, enumerate what is given:

83.23 degrees = angle formed by two stars
33 light years = distance from E to A
21 light years = distance from E to B

Use the cosine law to solve for the distance between two stars:
The opposite side of the angle 83.23 degrees is the distance between star A and star B.

D^2 = A^2 + B^2 - 2ABcos (x)

D^2 = 33^2 + 21^2 - (2*33*21*cos(83.23))

solve for D

D = 36.97 light years

Therefore, there are 36.97 light years between star A and star B.