Question

To find the height of the pole, a surveyor moves 200 feet away from the base of the pole and then, from an eye-level height of 6 feet, measures the angle of elevation to the top of the pole to be θ. Find the height of the pole to the nearest foot.

Option 1: 83
Option 2: 200
Option 3: 6
Option 4: θ

Answer 1

To find the height of the pole, we can use trigonometry and the concept of angle of elevation. In this scenario, the surveyor moves 200 feet away from the base of the pole and measures the angle of elevation, θ, from an eye-level height of 6 feet. We can set up a right triangle, where the height of the pole is the side opposite to the angle of elevation.

Step-by-step explanation:

To find the height of the pole, we can use trigonometry and the concept of angle of elevation. In this scenario, the surveyor moves 200 feet away from the base of the pole and measures the angle of elevation, θ, from an eye-level height of 6 feet. We can set up a right triangle, where the height of the pole is the side opposite to the angle of elevation.

We can use the tangent function to find the height of the pole. The tangent of the angle of elevation is equal to the ratio of the height of the pole to the distance from the base of the pole. So, we have:

tan(θ) = height / distance

Plugging in the values:

tan(θ) = height / 200

To isolate the height, we can multiply both sides of the equation by 200:

200 * tan(θ) = height

Now, we can substitute the given angle of elevation into the equation and calculate the height of the pole.