A triangle has three sides, meaning three vertices. A vertex is a point where two sides intersect. In a triangle, three vertices are joined by three independent segments, hence the edges. So a triangle with vertices a, b, and c.
The triangles are described by their length and internal angles. Now, if a triangle has three sides, it has equal lengths. It becomes an Equilateral triangle.
The Pythagorean theorem is specific to right-angle triangles.
For any right-angle triangle, the square of the hypotenuse length equals the sum of squares of lengths of two sides. It follows a rule that the sides must make it a right angle. While some other cases, such as 30°60°90° and 45°45°90° and 3,4, 5 these triangles facilitate the calculation.
Here a and b are two sides of a triangle, and c is the hypotenuse. The Pythagorean theorem can be written as:
a2 + b2 = c2.
Example: If a = 3, c = 5, now find b:
32 + b2 = 52
9 + b2 = 25
b2 = 16 => b = 4.
In other words, c=hypotenuse, and a and b will be the other sides of the triangle.
a2 + b2 = c2.
It is known as the Pythagorean equation. It was named after the Greek Philosopher Pythagoras. The formula is important because if sides of a triangle are known or given. The theorem can determine the lengths and angles if the other two sides' lengths and angles are given. So if the angle between the other sides of a right angle is given, the law of cosines reduces the Pythagorean Equation.
Some triangles are based on internal angles. These can be classified as oblique or right angles. A right triangle is one in which one angle is 90°. It is denoted by two lines forming a square at the vertex, making it a right angle. The longest edge of a triangle is the opposite edge of the right angle. It is called the hypotenuse. So any triangle that is not a right angle can be classified as either an oblique triangle or an Obtuse or acute angle.
A right triangle, in simple terms, has an angle that measures 90°. The relation and equation with the sides and angles are determining factors of trigonometry.
It has all the Greek symbols α(Alpha) and β (beta), which are used to measure unknown angles. In the calculator, h means the height or altitude of the triangle. It is the length of the vertex of the right angle. It is the hypotenuse of the triangle.
The altitude divides the triangle into two smaller triangles. It will form triangles similar to the original one. So all sides of the right-angle triangle have lengths called integers. It is called a Pythagorean triangle.
In a similar type of triangle, The three sides are collectively called the Pythagorean triple. For example:3, 4, 5; 5, 12, 13; 8, and others.
Any triangle's area and perimeter are calculated the same way as any other triangle. The perimeter is the sum of three sides of the triangle. The area can be calculated with the following formula.
A =1/2ab =1/2ch
The first one is a 30° 60° 90° triangle.
It refers to the angle measurements like 30°60°90°. So in this type of triangle, the sides correspond to angles 30°60°90°. They follow a ratio of 1:√3:2.
So in this type of triangle, if any side is known, the length of other sides can be calculated using the ratio given above.
Consider this as an example the side value is five, corresponding to the angle of 60°. Now consider "a" as the length corresponding to a 30° angle. Let's consider "b" as the length corresponding to 60° and "c" as the length of 90°
The following are the angles:
30° 60° 90°
The ratio of the sides: is 1:√3:2.
Length of the sides: a:5:c
Now use the known ratios of the sides of the triangle.
Now, with the above equation, it is clear that knowing one side of a 30°60°90° triangle helps you find the length of any other sides respectively. Now with this type of triangle, you can calculate trigonometric function for multiple of π/6.
The second one is a 45°45°90° triangle.
The 45°45°90° is a bit different than the 30°60°90°, and it is called an isosceles right triangle. It also has two sides with equal lengths. It is a right-angle triangle in which the sides correspond to angles 45°45°90°
It follows the ratio 1:1:√2.
Similar to the 30°60°90 triangle. It is important to know one side's length. It will help you find the length of the other sides of the 45°45°90° triangle.
Length of sides: a: a:c
Given information: c=5
A 45°45°90° triangle can help calculate the trigonometric functions with a multiple of π/4.
Effortlessly solve right triangle problems and explore special triangles with the powerful Right Triangle Calculator, simplifying your geometric calculations.
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