Jim stands beside a wide river and wonders how wide it is. he spots a large rock on the bank directly across from him. he then walks upstream 65 strides and judges that the angle between him and the rock, which he can still see, is now at an angle of 30o . jim measures his stride to be about 0.8 m long. estimate the width of the river.

To solve this problem, we must imagine that Jim’s initial position, the position of the rock, and Jim’s final position all connects to form a triangle. Now we can imagine that the triangle is a right triangle with the 90° angle on the initial position.

The angle of 30° is directly opposite to the length of his total stride while the width of the river is the side adjacent to the angle. Therefore can use the tan function to solve for the width of the river:

tan θ = opposite side / adjacent side

tan 30 = total stride distance / width of river

where total stride distance = 65 * 0.8 = 52 m

width of river = 52 m / tan 30

width of river = 90.07 m

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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