Question

karen, 5.5ft, 40ft, flagpole, 45°

Explanation:

Step1: Analyze the triangle type

The triangle formed by Karen's line of sight, the horizontal line, and the flagpole is a right - angled isosceles triangle (since one angle is \(45^{\circ}\) and one angle is \(90^{\circ}\), so the third angle is also \(45^{\circ}\)). In a right - angled isosceles triangle, the legs are equal. The horizontal distance from Karen to the flagpole is \(40\) ft, so the vertical height from Karen's eye level to the top of the flagpole is also \(40\) ft.

Step2: Calculate the total height of the flagpole

Karen's height is \(5.5\) ft. The height of the flagpole is the sum of Karen's height and the vertical height from her eye level to the top of the flagpole. So the height \(h=40 + 5.5\).

Answer:

The height of the flagpole is \(45.5\) ft.