- #1

- 1,009

- 0

## Homework Statement

Say I am dealing with a 45-45-90 deg angle

then sin(45 deg) = 1/(2)^(1/2)

What exactly is the value of 1/(2)^(1/2) referring to?

is is the measure of a side or what?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

In summary, the value of 1/(2)^(1/2) in reference to a 45-45-90 degree angle is the ratio of the length of the perpendicular to the length of the hypotenuse of the right angled triangle. This trigonometric ratio is independent of the size of the triangle and plays a crucial role in topics such as vector analysis, calculus, and Fourier analysis. Furthermore, it helps develop several other areas of mathematics beyond its initial definition as a ratio.

- #1

- 1,009

- 0

Say I am dealing with a 45-45-90 deg angle

then sin(45 deg) = 1/(2)^(1/2)

What exactly is the value of 1/(2)^(1/2) referring to?

is is the measure of a side or what?

Physics news on Phys.org

- #2

- 311

- 1

So, in a 45-45-90 triangle, the sides are 'a', 'a' and 'sqrt(2)*a.

So according to the above definition, sin(45) = a/sqrt(2)*a = 1/sqrt(2)

- #3

- 1,009

- 0

- #4

- 311

- 1

In fact, as you learn more, the dependency on a right angle triangle in defining sine and cos is completely removed. Given this, sines and cos retain the properties of the triangle without having anything to do it.

Trigonometric Functions have extreme importance in topics of vector analysis and calculus because of their very special properties. However, its major application comes in Fourier analysis, because of a theorem due to Fourier which states that

'every periodic function, can be written as a linear combination of sines and cosines.'

So you see, even though we begin with defining it as a ratio, it develops into something much more, which helps us develop several other areas of mathematics.

A 45-45-90 degree angle is a type of right triangle where the two shorter sides are equal in length and the longer side is equal to the square root of 2 times the length of the shorter sides. The three angles in this triangle measure 45 degrees, 45 degrees, and 90 degrees, respectively.

A 45-45-90 degree angle can be identified by its unique side lengths. The two shorter sides will be equal in length, and the longer side will be the square root of 2 times the length of the shorter sides. Additionally, the angles can be measured using a protractor to confirm that they are 45 degrees, 45 degrees, and 90 degrees.

The Pythagorean Theorem is a mathematical formula that states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In a 45-45-90 degree angle, the length of the longer side is equal to the square root of 2 times the length of the shorter sides, which follows the Pythagorean Theorem.

45-45-90 degree angles are commonly used in construction and engineering to create right angles and maintain symmetry in buildings and structures. They are also used in navigation and map-making to determine direction and distances between points. In mathematics, they are used to solve geometric problems and equations.

To calculate the missing side length in a 45-45-90 degree angle, you can use the Pythagorean Theorem or the special ratio of the sides (1:1:√2). For example, if the shorter sides are each 5 units in length, the longer side would be 5√2 units in length. To find a missing side, you can also use trigonometric functions such as sine, cosine, and tangent.

Share:

- Replies
- 5

- Views
- 1K

- Replies
- 1

- Views
- 424

- Replies
- 13

- Views
- 95

- Replies
- 7

- Views
- 454

- Replies
- 6

- Views
- 777

- Replies
- 11

- Views
- 1K

- Replies
- 18

- Views
- 1K

- Replies
- 5

- Views
- 2K

- Replies
- 3

- Views
- 839

- Replies
- 3

- Views
- 813