Using trigonometric functions first, show how to find the distance to the moon from earth and then find the radius of the moon. Secondly show how to find the distance from the sun to the planet Venus, consider the planets orbits to be circular for this.

If you could please answer and explain the question above. I seriously do not understand this.

Maria,

The question doesn't give enough information to know what your starting point is - what you "know" to begin with. If you know the masses of the earth and moon, then you can use gravitational force to calculate the orbital distance, but that's not trigonometric.

Here's a really contrived method: if you know the radius of the earth and If you can communicate with an observer several thousand miles away, then you can triangulate the distance. You'd need to calculate the length of the chord through the earth's mantle between the two of you observers, record (at the same moment in time), the angle between that chord and the sightline to an agreed-upon feature on the moon. The differences would be small, so you'd need to make accurate angular measurements. Then you'd have the angle, side and angle of a triangle and from that you can use the Law of Sines to figure out the length of the sight-lines. A little further geometry involving the sphere of the earth would give you the surface-to-surface distance.

Once you know the distance, calculating the radius of the moon is pretty easy to estimate by measuring the angle between the sightlines from an observer on earth to the opposite sides of the moon. If you make the reasonable assertion that the distance from you on earth to the side of the moon is about the same as the distance from you to the front of the moon, then the sine of that measured angle times the distance to the moon is roughly the moon's diameter.

Stephen La Rocque.>