- #1
Miike012
- 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?
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.