To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of
elevation to the top of the pole to be 44°44°. To the nearest foot, what is the height of the pole? (1 point)
135 feet
139 feet
149 feet
145 feet
To find the height of the pole, we can create a right triangle using the information given. The 140 feet away from the base of the pole is the adjacent side of the triangle, the height of the pole is the opposite side, and the distance from the top of the transit to the top of the pole (4 feet) is the opposite side.
Using the tangent function, we can calculate the height of the pole:
tan(44°) = height/140
height = 140*tan(44°)
height ≈ 140*0.966
height ≈ 135 feet
Therefore, to the nearest foot, the height of the pole is 135 feet. The answer is 135 feet.
135 is not it
Apologies for the oversight in my calculations. Let's try solving it again:
In the right triangle formed by the surveyor, the pole, and the line of sight to the top of the pole, we have:
tan(44°) = height of the pole / 140 feet
height of the pole = 140 feet * tan(44°)
height of the pole ≈ 140 feet * 0.966 = 135.24 feet
Rounded to the nearest foot, the height of the pole is 135 feet. So, the correct answer is 135 feet. Thank you for your patience.