To find the height of a pole, a surveyor moves 160 feet away from the base of the pole and then, with a transit 6 feet tall, measures the angle of elevation to the top of the pole to be 62°. To the nearest foot, what is the height of the pole?
A. 307 feet
B. 301 feet
C. 147 feet
D. 141 feet
We can use trigonometry to solve this problem. Let's draw a diagram:
The surveyor is standing 160 feet away from the base of the pole and measures an angle of elevation of 62 degrees to the top of the pole. We want to find the height of the pole, which we can call h.
We can use the tangent function:
tan(62 degrees) = h/160
We can multiply both sides by 160 to isolate h:
h = 160 tan(62 degrees)
Using a calculator, we get:
h ≈ 301 feet
Therefore, the answer is B. 301 feet to the nearest foot.
To find the height of the pole, we can use the tangent function and the given angle of elevation.
The tangent function is defined as the opposite side divided by the adjacent side of a right triangle.
In this problem, the opposite side is the height of the pole, and the adjacent side is the distance of the surveyor from the base of the pole.
Let's calculate the height using the tangent function:
tan(62°) = opposite/adjacent
tan(62°) = height/160
To find the height, rearrange the equation:
height = tan(62°) * 160
Using a calculator, calculate the approximate value of tan(62°):
tan(62°) ≈ 1.8807265
Now, substitute this value into the equation:
height ≈ 1.8807265 * 160
height ≈ 300.91624
Rounding to the nearest foot, the height of the pole is approximately 301 feet.
Therefore, the correct answer is B. 301 feet.
To find the height of the pole, we can use trigonometry. We can use the tangent function, which relates the opposite side of a right triangle (the height of the pole) to the adjacent side (the distance from the surveyor to the base of the pole).
First, let's label the given information:
- The distance from the base of the pole to the surveyor is 160 feet (adjacent side).
- The height of the transit is 6 feet.
Next, let's identify the angle of elevation, which is the angle between the ground and the line of sight from the surveyor to the top of the pole. In this case, the angle of elevation is given as 62°.
Now, we can use the tangent function to find the height of the pole:
tan(angle) = opposite/adjacent
tan(62°) = height/160
To isolate the height, we can rearrange the formula:
height = tan(62°) * 160
Using a calculator, we find:
height ≈ 307.172 feet
Since we are asked to round to the nearest foot, the height of the pole is approximately 307 feet.
Therefore, the correct answer is option A. 307 feet.
AAAaannndd the bot gets it wrong yet again!
Don't forget he's measuring the angle from 6' up.
(h-6)/160 = tan62°