Final answer:
To find the angle of elevation, use the tangent function. To find the height of the flagpole, use the tangent function again. To find the distance from the top of the flagpole to the observer, use the Pythagorean theorem. To find the length of the shadow, use similar triangles.
Step-by-step explanation:
To find the angle of elevation, we can use the tangent function. The angle of elevation is equal to the inverse tangent of the height of the flagpole divided by the distance from the observer to the base of the flagpole. So, angle of elevation = arctan(height/distance).
To find the height of the flagpole, we can use the tangent function again. The height of the flagpole is equal to the distance from the observer to the flagpole multiplied by the tangent of the angle of elevation. So, height = distance * tan(angle of elevation).
To find the distance from the top of the flagpole to the observer, we can use the Pythagorean theorem. The distance is equal to the square root of the sum of the height of the flagpole squared and the distance from the observer to the base of the flagpole squared. So, distance = sqrt(height^2 + distance^2).
To find the length of the shadow, we can use similar triangles. The length of the shadow is equal to the height of the flagpole multiplied by the distance from the observer to the base of the flagpole divided by the height of the observer. So, length of shadow = height * distance/observer height.