Aristarchus of samos measured the size of the moon relative to the size of the earth by measuring the maximum duration of a total lunar eclipse, from the beginning of the eclipse until the moon began to emerge from the earth's shadow. to estimate the size of the moon relative to the width of the earth's shadow, he also had to know

c. newton's third law of motion

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

conservation of mass

mass before something happens = mass afterwards