Question

The angle subtended by the moon's diameter at a point on the earth is about 0.5 degree use this and that that the moon is about 3 84000 km away to find the approximate diameter of the moon

Answer 1

For objects that subtend a relatively small angle (like 0.5) we can use the following approximation:

s = rθ

Where s is the actual diameter of the object in question, r is the distance to the object, and θ is the angle subtended by the object in the sky in radians

we must convert degrees to radians:

0.5º x (π / 180º) = 0.00873 rad

s = (384000000)(0.00873) = 3.35 x 10^6 m

Diameter of moon is 3.35 x 10^6 m

Answer 2

Answer:

For

objects that subtend a relatively small angle (like 0.5) we can use the following approximation:

s = rθ

Where

s is the actual diameter of the object in question, r is the distance

to the object, and θ is the angle subtended by the object in the sky in

radians

we must convert degrees to radians:

0.5º x (π / 180º) = 0.00873 rad

s = (384000000)(0.00873) = 3.35 x 10^6 m

Diameter of moon is 3.35 x 10^6 m