Question

?

Answer 1

start by drawing a point to represent Earth, then draw one line from earth to another point representing the star, then another point from Earth to the other star

then label the angle between them

lmk if you're having some trouble with this step

Answer 2

does it matter what side the stars or earth is on

Answer 3

not really

Answer 4

like, it should look something like a triangle with earth at one point, and the stars at the other two points

Answer 5

oh okay hold on

Answer 6

since they give you

1. distance between earth and star 1
and
2. distance between earth and star 2

it should be a bit more like this:

Answer 7

awesome, now label the distances given and the angle

Answer 8

oh is that alright

Answer 9

i did this looking at urs

Answer 10

yeah there should probably be a line between the stars haha

Answer 11

then just put the distances and angle on the diagram

Answer 12

okay will dothat

Answer 13

since it's the distances given it would be better to label the sides of the triangle rather than the points

Answer 14

23.30 is the distance between the earth and star A, not the distance between the stars

Answer 15

awesome now you just need the angle

Answer 16

awesome

now, since the problem asks for the distance between the stars A and B, you can use law of cosines to solve for the missing side

Answer 17

if we compare our system to the pink triangle we can see that

distance between the stars = c
a and b are 23.30 and 34.76
angle C = 76.04 degrees

so

c^2 = a^2 + b^2 - 2ab*cos(C) = ?

Answer 18

plugging everything in we get

c^2 = 23.30^2 + 34.76^2 - 2(23.30)(34.76)cos(76.04)

then just solve for c and the problem's done