Michael is standing in the middle of a playground at night looking at the American flag at the top of the flag pole. If he knows he is 50 feet away from the base of the flag pole and his father told him the pole is 100 feet tall, what is the angle that Michael is looking up relative to the ground?
tan x = 100/50
Tan x=(100/50)
so
X= Tan^-1(100/50), you have to use the inverse of tan
therefore,
x=63.435
To find the angle that Michael is looking up relative to the ground, we can use the concept of trigonometry. Specifically, we can use the tangent function, which relates the angle of interest to the sides of a right triangle.
Let's consider a right triangle formed by Michael, the flagpole, and the ground. The height of the flagpole is given as 100 feet, and Michael is standing 50 feet away from the base of the flagpole. The angle that Michael is looking up is the angle opposite to the height of the flagpole in the right triangle.
Using the tangent function, we can express this relationship as:
tan(angle) = height of flagpole / distance from flagpole
Substituting the known values:
tan(angle) = 100 feet / 50 feet
Simplifying:
tan(angle) = 2
To find the angle itself, we need to take the arctangent (inverse tangent) of both sides:
angle = arctan(2)
Using a calculator or trigonometric table, we find that the arctangent of 2 is approximately 63.43 degrees.
Therefore, the angle that Michael is looking up relative to the ground is approximately 63.43 degrees.