To find the height of a pole, a surveyor moves 120 feet away from the base of the pole and then, with a transit 8 feet tall, measures the angle of elevation to the top of the pole to be 36°. To the nearest foot, what is the height of the pole?(1 point)
Responses
79 feet
79 feet
87 feet
87 feet
95 feet
95 feet
71 feet
To find the height of the pole, we can use the tangent of the angle of elevation.
First, we need to find the height of the pole above the surveyor's eye level. This can be calculated by:
Height of pole = 120 feet * tan(36°)
Height of pole = 120 ft * tan(36°)
Height of pole = 120 ft * 0.7265
Height of pole ≈ 87 feet
Since the height of the transit is 8 feet, the total height of the pole would be:
Total height of pole = Height of pole + height of the transit
Total height of pole = 87 feet + 8 feet
Total height of pole ≈ 95 feet
Therefore, the height of the pole is approximately 95 feet.