trig pls.. help me

A rocket carrying a weather satellite is launched. As it moves through space, the rocket is tracked by two tracking stations located 24 km. apart, beneath the rocket. The 2 tracking stations both lie west of the launching pad. at a specific moment, the rocket's angle of elevation from Station X is 40 deg. while the rocket's angle of elevation from Station Y is 70 deg. Both tracking stations are west of the rocket at this moment. At this moment, what is the altitude of the rocket, correct to one decimal place?

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asked by Mhy
  1. make a sketch, on a straight line mark off points
    X, Y, and Z, where Z is then end of the altitude SZ, where S is the satellite.
    Angle X = 40°
    angle SYZ=70°
    XY = 24

    in triangle XYS,
    angle x=40, angle XYS = 110 , and angle XSY = 30°
    by the sine law:
    YS/sin40 = 24/sin30
    YS = 30.8538

    in right-angled triangle SYZ,
    RZ/30.8538 = cos 70
    RZ = 10.55

    the height is appr. 10.6 km

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    posted by Reiny
  2. thank you so much...

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    posted by Mhy

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