Question

A satellite, which you can assume to be spherical, has a diameter of 12 m. If it subtends an angle of 0.0014° to an observer on Earth, find the distance to the satellite, giving your answer to two significant figures.

Answer 1

the diameter of satellite ,and observer form a scalene traiangle made up of two right triangles, the distnace from the observer to the satellite form one side which bisects the angle 0.0010 which is 0.0005degrees.

the other side is half the diameter of the satellite or 5.5meters

assign the angles and sides as follows:

A=0.0005 degrees

a=5.5m

B=180-90-0.0005=89.9995degrees

b=the distance from the observer to satellite

using the law of sines

[b/sin(89.9995)] = [5.5/sin(0.0005)]

b=5.5 sin(89.9995)/sin(0.0005)

b=6302253.57meters which is 630.25km