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102 LearnersLast updated on September 11, 2025
45 45 90 Triangle Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you're cooking, tracking BMI, or planning a construction project, calculators can make your life easy. In this topic, we are going to talk about the 45 45 90 triangle calculator.
What is a 45 45 90 Triangle Calculator?
A 45 45 90 triangle calculator is a tool to determine the sides of a right-angled isosceles triangle, where the angles are 45°, 45°, and 90°. This type of triangle has sides in a specific ratio, which allows for easy calculations of side lengths when one side is known.
How to Use the 45 45 90 Triangle Calculator?
Below is a step-by-step process on how to use the calculator:
Step 1: Enter the length of one side: Input the known side length into the given field.
Step 2: Click on calculate: Click on the calculate button to compute the other sides.
Step 3: View the result: The calculator will display the lengths of the other sides instantly.
How to Calculate the Sides of a 45 45 90 Triangle?
In a 45 45 90 triangle, the sides are in the ratio 1:1:√2.
This means: If one leg of the triangle is x, then:
The other leg is also x.
The hypotenuse is x√2. Therefore, the formulas are:
Leg = x - Hypotenuse = x√2
This ratio allows for quick calculations of unknown sides when one side is known.
Tips and Tricks for Using the 45 45 90 Triangle Calculator
When using a 45 45 90 triangle calculator, consider these tips and tricks to avoid mistakes:
Remember that the legs of the triangle are always equal.
Use the ratio 1:1:√2 for faster mental calculations.
Ensure your calculator is set to use the correct units (e.g., degrees for angles).
Common Mistakes and How to Avoid Them When Using the 45 45 90 Triangle Calculator
Even when using a calculator, mistakes can happen. Here are some common errors and how to avoid them when using a 45 45 90 triangle calculator.
Mistake 1
Incorrectly calculating the hypotenuse
Be sure to multiply the length of a leg by √2 to find the hypotenuse. Forgetting to use the √2 factor will result in an incorrect hypotenuse length.
Mistake 2
Confusing the legs and hypotenuse
Remember that in a 45 45 90 triangle, the hypotenuse is the longest side and is opposite the 90° angle. Do not confuse it with the legs, which are equal.
Mistake 3
Forgetting that the legs are equal
A common mistake is assuming the legs are different. In a 45 45 90 triangle, the legs are always the same length.
Mistake 4
Not using the correct degree of precision
While calculating, make sure to use appropriate precision for square roots to avoid significant errors in the results.
Mistake 5
Assuming all calculators provide exact values
Remember that some calculators may give approximations for square roots. Double-check the results if precision is critical.
45 45 90 Triangle Calculator Examples
Problem 1
What are the sides of a 45 45 90 triangle if one leg is 5 units long?
Use the formulas:
Leg = 5
Hypotenuse = 5√2 ≈ 7.07
If one leg is 5 units, the hypotenuse will be about 7.07 units.
Explanation
By using the ratio 1:1:√2, if one leg is 5, the other leg is also 5, and the hypotenuse is calculated as 5√2.
Problem 2
A square garden has a diagonal of 14 meters. What is the side length of the garden?
For a square, the diagonal forms a 45 45 90 triangle.
Hypotenuse = 14
Leg = 14/√2 ≈ 9.9
Each side of the garden is about 9.9 meters.
Explanation
Using the hypotenuse to leg calculation, divide the diagonal by √2 to find the side of the square.
Problem 3
You have a kite in the shape of a 45 45 90 triangle. If the hypotenuse is 10 cm, what are the lengths of the legs?
Hypotenuse = 10
Leg = 10/√2 ≈ 7.07
Each leg of the kite is about 7.07 cm.
Explanation
Divide the hypotenuse by √2 to find the length of each leg based on the 1:1:√2 ratio.
Problem 4
If a 45 45 90 triangle has legs of 12 cm, what is the length of the hypotenuse?
Leg = 12
Hypotenuse = 12√2 ≈ 16.97
The hypotenuse is about 16.97 cm.
Explanation
Multiply the leg length by √2 to find the hypotenuse in a 45 45 90 triangle.
Problem 5
An isosceles right triangle has a leg length of 8 units. What is the hypotenuse?
Leg = 8 Hypotenuse = 8√2 ≈ 11.31
The hypotenuse is approximately 11.31 units.
Explanation
Using the formula for the hypotenuse, multiply the leg by √2 to determine its length.
FAQs on Using the 45 45 90 Triangle Calculator
1.How do you calculate the hypotenuse of a 45 45 90 triangle?
2.Are the legs of a 45 45 90 triangle always equal?
3.Why is the ratio 1:1:√2 used for a 45 45 90 triangle?
4.How do I use a 45 45 90 triangle calculator?
5.Is the 45 45 90 triangle calculator accurate?
Glossary of Terms for the 45 45 90 Triangle Calculator
- 45 45 90 Triangle: A special type of right triangle with angles of 45°, 45°, and 90°.
- Leg: Either of the two equal sides in a 45 45 90 triangle.
- Hypotenuse: The longest side of a right triangle, opposite the right angle.
- √2: The square root of 2, an irrational number approximately equal to 1.414.
- Isosceles Right Triangle: Another name for the 45 45 90 triangle, indicating two equal sides.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
