Final answer:
To determine the height of the pole, we use the tangent function with the given angle of elevation and distance from the pole, then add Leon's eye level to find the total height, which is rounded to the nearest tenth.
Step-by-step explanation:
Leon is standing 27 feet from a utility pole and sees a red-tailed hawk on top of the pole with an angle of elevation of 25 degrees. His eyes are 4 feet above the ground. To find the height of the pole, we can use trigonometry, specifically the tangent function.
Tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, the opposite side is the height of the pole above Leon's eyes, and the adjacent side is the distance from Leon to the pole. The equation is:
tan(25 degrees) = (height of pole above eyes) / 27 feet
Multiply both sides by 27 feet to solve for the height above Leon's eyes:
27 feet * tan(25 degrees) = height of the pole above eyes
Calculate the tangent and multiply to find the height above Leon's eyes, then add the height of Leon's eyes above the ground (4 feet) to find the total height of the pole.
The height of the pole rounded to the nearest tenth of a foot is given as: