A 38 foot tree casts a 16 foot shadow what is the angle of elavation of the sun to the nearest degree?
looks like
tanØ = 38/16
Ø = appr 67°
To determine the angle of elevation of the sun, you can use trigonometry. The angle of elevation is the angle between the horizontal ground and the line of sight to the top of the tree. In this case, we have a right triangle formed by the tree, its shadow, and the sun's rays.
Let's label the sides of the triangle:
- The height of the tree is the opposite side (O) and has a length of 38 feet.
- The length of the shadow is the adjacent side (A) and has a length of 16 feet.
The tangent function (tan) can be used to find the angle of elevation:
tan(angle) = opposite/adjacent
tan(angle) = O/A
Substituting the known values:
tan(angle) = 38/16
Now, we can calculate the angle by taking the inverse tangent (arctan) of both sides:
angle = arctan(tan(angle))
angle = arctan(38/16)
Using a calculator, we find that arctan(38/16) ≈ 67.38 degrees.
Therefore, the angle of elevation of the sun to the nearest degree is 67 degrees.