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 find the angle at which the rays of the sun hit the ground, we can use trigonometry. In this case, we will use the tangent function.
The tangent of an angle can be calculated by dividing the length of the opposite side by the length of the adjacent side.
In this scenario, the tree is the opposite side, and its shadow is the adjacent side. Since we know that the tree is 100 feet tall and its shadow is 150 feet long, we can set up the following equation:
tangent(angle) = height of the tree / length of the shadow
tangent(angle) = 100 / 150
Now, we can take the inverse tangent (also known as arctan or atan) of both sides to isolate the angle:
angle = atan(100 / 150)
Using a calculator, we can find the inverse tangent of 100/150 to be approximately 33.69 degrees.
Hence, the angle at which the rays of the sun hit the ground, to the nearest degree, is 34 degrees.