Interesting angles between 10~~25º ?

• I
• Nik_2213
In summary, the conversation discusses the concept of "interesting" angles between 10~~25º, with various suggestions such as small angles, irrational angles, and angles that can be constructed with a compass and ruler. The definition of "interesting" is also debated, with one suggestion being angles whose sine is in a Galois extension of ##\mathbb{Q}.##
Nik_2213
TL;DR Summary
Just as there are 'interesting' numbers, per primes, Pythag' triples etc, are there any 'interesting' angles between 10~~25º ??
NOT a home-work / college question, merely wondering...

Just as there are 'interesting' numbers, per primes, Pythag' triples, Euler-stuff etc, are there any 'interesting' angles between 10~~25º ??

I've had a hunt around, noticed several possibilities invoking eg transcendental fractions of radians etc, but...

Ideas ??

Combinations starting with 45 and 30 might be of interest.

Nik_2213 said:
are there any 'interesting' angles between 10~~25º ??
Define "interesting"

phinds said:
Define "interesting"
inter esse, lat. being between

Astronuc, mfb, jedishrfu and 2 others
Irrational angles might be interesting.

Last edited:
jedishrfu
12 = 60/5 ~ pi/15
15 = 60/4 ~ pi/12
20 = 60/3 ~ pi/9
22.5 = 90/4 ~ pi/8

bob012345
bob012345 said:
Irrational angles might be interesting.
Almost all angles are irrational.

bob012345
pbuk said:
Almost all angles are irrational.
It might be interesting that one can make by construction irrational angles and line segments.

How about: An angle is called interesting iff its sine is in a Galois extension of ##\mathbb{Q}.##

fresh_42 said:
How about: An angle is called interesting iff its sine is in a Galois extension of ##\mathbb{Q}.##
Sorry, I dozed off there. What were you saying again?

jbriggs444 said:
Sorry, I dozed off there. What were you saying again?
That we can draw the darn thing with compass and ruler.

malawi_glenn, pbuk and jbriggs444

1. What are interesting angles between 10˚ and 25˚?

Interesting angles between 10˚ and 25˚ are angles that fall within this range and have unique properties or applications. These angles are often seen in geometry, trigonometry, and real-world situations such as architecture and engineering.

2. How do you find the measure of an angle between 10˚ and 25˚?

To find the measure of an angle between 10˚ and 25˚, you can use a protractor or a compass and ruler to measure the angle directly. Alternatively, you can use trigonometric functions such as sine, cosine, or tangent to calculate the angle's measure based on the given information.

3. What are some real-life examples of interesting angles between 10˚ and 25˚?

Real-life examples of interesting angles between 10˚ and 25˚ include the angle of inclination of the Leaning Tower of Pisa, the angle of elevation of a ladder against a building, and the angle of a ramp for wheelchair accessibility. These angles have practical applications in architecture, construction, and accessibility design.

4. Why are angles between 10˚ and 25˚ important in mathematics?

Angles between 10˚ and 25˚ are important in mathematics because they represent a wide range of angles that are commonly used in various mathematical concepts and applications. These angles are often used to calculate distances, heights, and other measurements, making them essential in fields such as geometry, trigonometry, and physics.

5. Can angles between 10˚ and 25˚ be classified as acute, obtuse, or right?

Yes, angles between 10˚ and 25˚ can be classified as acute, obtuse, or right. An acute angle is less than 90˚, an obtuse angle is between 90˚ and 180˚, and a right angle is exactly 90˚. Depending on their measure, angles between 10˚ and 25˚ can fall into any of these categories.

Replies
8
Views
3K
Replies
6
Views
2K
Replies
20
Views
2K
Replies
3
Views
1K
Replies
1
Views
2K
Replies
8
Views
2K
Replies
2
Views
6K
Replies
1
Views
2K
Replies
7
Views
2K
Replies
5
Views
4K