A tree that is 100 feet tall casts a shadow that is 150 feet long. Determine the angle at which the rays of the sun hit the ground to the nearest degree.

To determine the angle at which the rays of the sun hit the ground, we can use the trigonometric concept of tangent.

The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.

In this scenario, the opposite side is the tree's height, which is 100 feet, and the adjacent side is the length of the shadow, which is 150 feet.

So, we have:

tan(angle) = opposite/adjacent
tan(angle) = 100/150

To find the angle itself, we can use the inverse tangent function (denoted as tan^(-1)):

angle = tan^(-1)(100/150)

Using a calculator, we get:

angle = 33.69 degrees (rounded to the nearest degree)

Therefore, the angle at which the rays of the sun hit the ground is approximately 34 degrees.

To determine the angle at which the rays of the sun hit the ground, we can use trigonometry. Specifically, we can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In this case, the height of the tree represents the length of the opposite side, and the length of the shadow represents the length of the adjacent side.

Let's label the height of the tree as 'h' and the length of the shadow as 's'. In this case, h = 100 feet and s = 150 feet.

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. Therefore:

tan(angle) = opposite/adjacent = h/s

Now, let's substitute the values we have:

tan(angle) = 100/150

To find the angle, we can take the inverse tangent (also known as arctangent or tan^-1) of both sides:

angle = arctan(100/150)

Using a scientific calculator, you can evaluate this expression to find the angle. In this case, the angle is approximately 33.69 degrees.

Therefore, the angle at which the rays of the sun hit the ground is approximately 33 degrees (to the nearest degree).

34

tan(x) = 100/150

x = arctan(2/3) = 34°