1. What is a 45-45-90 Triangle Calculator?
Definition: This calculator computes the sides, area, and perimeter of a 45-45-90 triangle given the length of one leg .
Purpose: It is used in geometry and engineering to determine the properties of a 45-45-90 triangle, which is an isosceles right triangle with fixed side ratios.
2. How Does the Calculator Work?
The calculator uses the following formulas for a 45-45-90 triangle, where is one of the legs:
- Leg : (since the triangle is isosceles)
- Hypotenuse :
- Area:
- Perimeter:
Unit Conversions:
- Input Dimensions: m, cm (1 m = 100 cm), mm (1 m = 1000 mm), in (1 m = 39.3701 in), ft (1 m = 3.28084 ft), yd (1 m = 1.09361 yd)
- Output Sides and Perimeter: m, cm, mm, in, ft, yd
- Output Area: m², cm² (1 m² = 10000 cm²), mm² (1 m² = 1000000 mm²), in² (1 m² = 1550.0031 in²), ft² (1 m² = 10.7639 ft²), yd² (1 m² = 1.19599 yd²)
Steps:
- Input the length of leg with its unit.
- Convert the dimension to meters for calculation.
- Calculate , , area, and perimeter using the formulas.
- Convert each result to its respective selected unit for display, using scientific notation for values less than 0.001, otherwise with 4 decimal places.
3. Importance of 45-45-90 Triangle Calculations
Calculating the properties of a 45-45-90 triangle is crucial for:
- Geometry Education: Understanding special triangles and their properties.
- Engineering Design: Using isosceles right triangles in structural components.
- Trigonometry Applications: Simplifying calculations involving 45° angles.
4. Using the Calculator
Examples:
- Example 1: For a triangle with :
- Convert:
- Leg :
- Hypotenuse :
- Area:
- Perimeter:
- Convert: , , Area = , Perimeter =
- Example 2: For a triangle with :
- Convert:
- Leg :
- Hypotenuse :
- Area:
- Perimeter:
- Convert: , , Area = , Perimeter =
5. Frequently Asked Questions (FAQ)
Q: What is a 45-45-90 triangle?
A: A 45-45-90 triangle is an isosceles right triangle with two 45° angles and one 90° angle, where the legs are equal, and the hypotenuse is times the leg length.
Q: Why are 45-45-90 triangles important?
A: They have consistent side ratios, making them useful in trigonometry, geometry, and engineering for simplifying calculations.
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