two sightings of the top of a flagpole are taken 75 meters apart on level ground. The two sightings are 21° and 32°. What is the height of the flagpole?
Draw a diagram, then take a look at the cot function and you will see that
h cot21° - h cot32° = 75
To find the height of the flagpole, we can use trigonometry. Let's consider the triangle formed by the height of the flagpole, the distance between the sightings (75 meters), and the angles of elevation.
We have two angles of elevation: 21° and 32°. The opposite side of the angles is the height of the flagpole, and the adjacent side is the distance between the sightings (75 meters).
Using the tangent function, we can set up the following equations:
For the first sighting (21°):
tan(21°) = height of the flagpole / 75 meters
For the second sighting (32°):
tan(32°) = height of the flagpole / 75 meters
To find the height of the flagpole, we can solve these equations simultaneously.
Step 1: Calculate the tangent values for 21° and 32°
tan(21°) ≈ 0.389
tan(32°) ≈ 0.624
Step 2: Set up the equations:
0.389 = height of the flagpole / 75 meters
0.624 = height of the flagpole / 75 meters
Step 3: Solve for the height of the flagpole:
height of the flagpole = 0.389 * 75 meters ≈ 29.175 meters
(height of the flagpole = 0.624 * 75 meters ≈ 46.8 meters)
Therefore, the height of the flagpole is approximately 29.175 meters.