Question

PLEASEEEEE HELP ASAP!!! IM NOT GOOD AT MATH AND I DONT UNDERSTAND THIS PROBLEM!!!! PLEASE HELP!!!!!

You observe two moons orbiting a planet. The moons are 750,000 miles from each other and equidistant from the planet as shown below.



Which expression below is equivalent to how many miles each moon is from the planet?


the answer choices are the expressions down below in the pictures.

Answer 1

You need to use the law of sines.
First, we find the measures of the angles x.
x + x + 100 = 180
2x + 100 = 180
2x = 80
x = 40

Now we set up an equation based on the law of sines.


`(a)/(\sin A) = (b)/(\sin B) = (c)/(\sin C)`

We know one angle (100 deg) and its opposite side (750,000 miles).
Then we know another angle (40 deg) and need to find the opposite side (d).


`(d)/(\sin 40^\circ) = (750,000)/(\sin 100^\circ)`

Now we solve for d. Multiply both sides by sin 40.


`d = (\sin 40^\circ)/(\sin 100^\circ) * 750,000`

Answer: The first choice.