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Find the angle so that it seems that Mars is approaching to you

Homework Statement
The spaceship S approaches Mars following the trajectory ##b−b## with velocity ##19.3 km/s## with respect to the Sun. If Mars has a velocity ##24.1 km/s## along the trajectory ##a−a## with respect to the Sun and the angle between ##b-b## and ##a-a## is ##30°## determine the angle between ##SM## and ##b−b## such that a person inside the spaceship "sees" that Mars is moving towards him
Homework Equations
##v_{M/S}=v_M - v_S##.
I know that ##v_{M/S}=v_M - v_S##. I also know that ##v_M = (-24.1;0)##. Then, using some trigonometry, ##v_S=(-19.3 sin 30°;19.3 cos 30°)##.
So I can find ##v_{M/S}##. But that doesn't tell me anything about the angle ##\beta##.
 

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You have all three sides of a triangle, you can find the angles.
 
You have all three sides of a triangle, you can find the angles.
What triangle are you talking about? The one formed by the ##v_S##, ##v_M## and ##v_{M/S}##?
 
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Yes. The time until you and Mars collide is fixed, so distances and velocities are proportional to each other.
 

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