when the full moon directly overhead the angle from one edge of the moon to the other is measured to be 0.6970 if the diameter of the moon is 3650 km how far is it from the moon

you know that s = rθ

Plug in your numbers. Remember that θ is in radians, which your value clearly is not.

To determine the distance from the moon, we can use basic trigonometry and the given information about the angle and diameter of the moon.

First, let's visualize the scenario. Imagine you are standing on the Earth's surface and looking up at the full moon when it is directly overhead.

Now, consider the moon as a circle, with the diameter representing a line passing through the center of the moon. The angle from one edge of the moon to the other, when measured from your perspective on Earth, is 0.6970 radians.

Using this information, we can set up a right triangle. The hypotenuse of the triangle represents the distance from the Earth to the moon, the adjacent side represents half of the moon's diameter, and the angle we have is opposite to the half-diameter.

Let's define the variables:
d = distance from the moon (what we want to find)
θ = angle from one edge of the moon to the other (0.6970 radians)
r = radius of the moon (half of the diameter, 3650 km / 2 = 1825 km)

Now, let's calculate the distance (d) using trigonometry.

tan(θ) = r / d

Since we know θ and r, we can rearrange the equation to solve for d:

d = r / tan(θ)

Substituting the values:

d = 1825 km / tan(0.6970 radians)

Using a scientific calculator or an online trigonometric calculator, you can find the value:

d ≈ 255,432 km

So, the distance from the moon, when the full moon is directly overhead, is approximately 255,432 kilometers.