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.
[tex] \dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C} [/tex]
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).
[tex] \dfrac{d}{\sin 40^\circ} = \dfrac{750,000}{\sin 100^\circ} [/tex]
Now we solve for d. Multiply both sides by sin 40.
[tex] d = \dfrac{\sin 40^\circ}{\sin 100^\circ} \times 750,000 [/tex]
Answer: The first choice.
