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Right Triangle Formula
A triangle is a closed figure with 3 sides, 3 angles and 3 vertices and for right triangles formulas, the properties have to be more specific. If any one of the angles of a triangle is a right angle measuring 90°, the triangle is called a right angled triangle or simply, a right triangle.
A right triangle formula would help you solve variety calculations related to the perimeter area, etc of the right triangle.
What are the Right Triangles Formulas?
A right-angled triangle is one which has one of its interior angles measuring 90 degrees. Right angled triangle formulas are used to calculate the perimeter, area, height, etc of a right triangle using its three sides.
Pythagoras theorem: (Hypotenuse)² =(Altitude)² + (Base)²
Area = 1//2 × base altitude
Perimeter = Hypotenuse + Base + Altitude.
Right Angled Triangle Formula:
Different formulas associated with the right triangle are:
- Pythagoras theorem formula definition shows relations among the three sides of a right triangle. The square of the hypotenuse is equal to the sum of squares of the other two sides.
(Hypotenuse)² =(perpendicular)² +(Base)²
- Area of a right triangle formula is given as
Area =1/2 × Base height = ½ × b h
Where height, h is equal to the length of the perpendicular side of the triangle.
- The perimeter of a right triangle formula is given as
Perimeter = a + b + c
Where a, b and c are the three sides of the triangle.
Example:
Question: The length of the base and perpendicular of a right-angled triangle is 6 in and 3 in respectively. Find the length of its hypotenuse, the perimeter of the triangle and area of the triangle.
Solution:
Length of base =6 in, length of perpendicular = 8 in
1. Using Pythagoras’ theorem,
(Hypotenuse)² = (Base)² + (Perpendicular)²
(Hypotenuse)² = 6² +8² = 100
Hypotenuse = √100 = 10 in
2. Using the perimeter of a right triangle formula,
Perimeter = 6+8+10= 24in
3. Using the area of triangle formula
Area= (1/2) b ×h
(1/2) ×6 × 8 = 24in².
