Trigonometry Problem: Height of a Pole Calculation
What is the height of the pole?
To find the height of a pole, a surveyor uses a theodolite that is 4 ft tall. The surveyor stands 140 feet away from the base of the pole, and measures the angle of elevation to the top of the pole to be 44°. Round the answer to the nearest foot. a. 143 ft b. 135 ft c. 147 ft d. 139 ft
Final answer:
The height of the pole can be found using trigonometry: the tangent of the angle times the distance. Considering also the height of the theodolite, the nearest possible answer would be 135ft.
Explanation:
This problem can be solved using basic trigonometry. It involves the concept of a right triangle and the use of the tangent function. Given the information provided, we know the angle of elevation is 44° and the horizontal distance from the pole is 140 feet. Remember that the theodolite is 4ft tall, so when calculating the pole's height, we need to add this height to the result.
The height can be calculated using the formula: height = tan(angle) * distance. In this case, height = tan(44) * 140 = 132.3ft (rounded to the nearest foot). When accounting for the theodolite's height, the total height of the pole is 132 + 4 = 136ft.
Therefore, the closest answer from the options given would be option b. 135ft.