Question

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?

Answer 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

Answer 2

thank you so much...