Question

you measure the shadow of the tree when the sun is at a 65 degree angle of elevation. the trees shadow measures 45 degrees feet long. how tall is the tree? the bin is 50 feet tall and the auger is 91 feet long. what angle does the auger form with the grain bin?

Answer 1

To find the height of the tree, use the formula: Tree Height = Shadow Length / Tan(Angle of Elevation). The height of the tree is approximately 24.6 feet. To find the angle formed by the auger with the grain bin, use the formula: Angle = Inverse Tan(length of auger / height of grain bin). The angle is approximately 61.5 degrees.

Step-by-step explanation:

To find the height of the tree, we can use trigonometry. Since we have the length of the tree's shadow and the angle of elevation of the sun, we can use the tangent function. The formula to find the height of the tree is:

Tree Height = Shadow Length / Tan(Angle of Elevation)

Substituting the values given: Shadow Length = 45 feet and Angle of Elevation = 65 degrees, we can calculate the height of the tree.

Tree Height = 45 feet / Tan(65 degrees).

Using a scientific calculator, the height of the tree is approximately 24.6 feet.

To find the angle formed by the auger with the grain bin, we can use the inverse tangent function. The formula is:

Angle = Inverse Tan(length of auger / height of grain bin).

Substituting the values given: Length of auger = 91 feet and Height of grain bin = 50 feet, we can calculate the angle formed by the auger with the grain bin.

Angle = Inverse Tan(91 feet / 50 feet).

Using a scientific calculator, the angle formed by the auger with the grain bin is approximately 61.5 degrees.