A flagpole casts a shadow 44 ft with the sun angle of elevation is 60.5 degrees. Find the height of the

flagpole and at what angle is the shadow twice as long?

if the flagpole has height h,

h/44 = tan 60.5°
h = 77.77

now you want the angle x where
77.77/88 = tan x
x = 41.5°

To find the height of the flagpole, we can use the tangent function:

Step 1: Determine the length of the shadow and the angle of elevation.
Given:
- Shadow length: 44 ft
- Angle of elevation: 60.5 degrees

Step 2: Use the tangent function to find the height.
The tangent function relates the angle of elevation to the height and shadow length:
tan(angle) = height / shadow length

Since we want to find the height, we can rearrange the formula to solve for height:
height = tan(angle) * shadow length

Now we can substitute the values into the formula:
height = tan(60.5 degrees) * 44 ft

Using a scientific calculator, we evaluate:
height ≈ 96.49 ft

Therefore, the height of the flagpole is approximately 96.49 ft.

To find the angle at which the shadow is twice as long, we need to consider the relationship between the angle of elevation and the shadow length.

Step 1: Let x represent the angle we are trying to find.

Step 2: Use the tangent function to relate the angle of elevation, height, and shadow length:
tan(x) = height / (2 * shadow length)

Since we want to find the angle x, we can rearrange the formula to solve for x:
x = arctan(height / (2 * shadow length))

Now we can substitute the values into the formula:
x = arctan(96.49 ft / (2 * 44 ft))

Using a scientific calculator, we evaluate:
x ≈ 63.26 degrees

Therefore, the angle at which the shadow is twice as long is approximately 63.26 degrees.