A mariner using a descendant of the astrolabe called an “octant.” Courtesy NOAA
The mariner’s astrolabe is an ancient navigation instrument for measuring celestial altitude (celestial altitude is the “height” of a star, planet or other celestial object above the horizon). Celestial altitude is important to mariners, because it provides a way to estimate geographic latitude, which is a location’s distance from the equator.
Astrolabes were the most popular astronomical instrument for several centuries, but they eventually were replaced by quadrants, which today have been replaced by sextants.
The height of the flagpole is side A plus “H” which is the height of your eyeball above the ground.
The tangent of angle a is equal to side A divided by side B. Written in the shorthand way: tan a = A ÷ B
Suppose angle a is equal to 60° and side B is 50 feet. Then, tan 60° = A ÷ 50 feet
You can find tangents on many calculators, and in tables from trigonometry books and on the internet. The tangent of 60° is 1.73. So, 1.73 = A ÷ 50 feet
So, A is equal to 1.73 multiplied by 50, which is 86.5 feet
The height of the flagpole is side A plus “H” which is the height of your eyeball above the ground. If H is equal to 4.5 feet, the height of the flagpole is: 86.5 ft + 4.5 ft = 91 feet