90 Triangle Calculator

Right triangles are among the most common and useful shapes in mathematics, geometry, engineering, and construction. Whether you are a student learning the Pythagorean theorem, a builder measuring materials, or a math enthusiast exploring trigonometry, being able to quickly calculate the missing sides and angles of a right triangle is extremely valuable.

90° Triangle Calculator

What is a 90° Triangle?

A 90° triangle (also called a right triangle) is a special type of triangle where one angle is exactly 90 degrees. The side opposite the right angle is known as the hypotenuse, while the other two sides are called legs.

According to the Pythagorean theorem: c2=a2+b2c^2 = a^2 + b^2c2=a2+b2

Where:

  • c = hypotenuse
  • a = leg A
  • b = leg B

This formula allows us to calculate the missing side and solve many geometric problems.

🔹 Features of the 90° Triangle Calculator

Our tool is designed for simplicity and accuracy. Here’s what it offers:

✅ Instant Calculations – No need for manual formulas. Enter values and get results instantly.
✅ Find Hypotenuse – Automatically computes the hypotenuse using the Pythagorean theorem.
✅ Calculate Area – Quickly determines the triangle’s area.
✅ Get Perimeter – Sums all three sides to give total perimeter length.
✅ Angles Finder – Shows the two acute angles based on trigonometric ratios.
✅ Reset Option – Clear inputs and start over with one click.

🔹 How to Use the 90° Triangle Calculator

Using the calculator is very straightforward. Follow these steps:

  1. Enter the values of Leg A and Leg B into the input fields.
    • Example: Leg A = 3, Leg B = 4
  2. Click the "Calculate" button.
  3. Instantly see the results:
    • Hypotenuse (c)
    • Area
    • Perimeter
    • Angle opposite Leg A
    • Angle opposite Leg B
  4. If you want to start again, click the "Reset" button.

🔹 Example Calculation

Let’s take a classic example:

  • Leg A = 3
  • Leg B = 4

Step 1: Calculate the Hypotenuse

c=a2+b2=32+42=9+16=25=5c = \sqrt{a^2 + b^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5c=a2+b2​=32+42​=9+16​=25​=5

Step 2: Calculate the Area

Area=12×a×b=12×3×4=6\text{Area} = \frac{1}{2} \times a \times b = \frac{1}{2} \times 3 \times 4 = 6Area=21​×a×b=21​×3×4=6

Step 3: Calculate the Perimeter

Perimeter=a+b+c=3+4+5=12\text{Perimeter} = a + b + c = 3 + 4 + 5 = 12Perimeter=a+b+c=3+4+5=12

Step 4: Calculate Angles

  • Angle opposite Leg A:

θ=arctan⁡(ab)=arctan⁡(34)≈36.87°\theta = \arctan\left(\frac{a}{b}\right) = \arctan\left(\frac{3}{4}\right) ≈ 36.87°θ=arctan(ba​)=arctan(43​)≈36.87°

  • Angle opposite Leg B:

θ=arctan⁡(ba)=arctan⁡(43)≈53.13°\theta = \arctan\left(\frac{b}{a}\right) = \arctan\left(\frac{4}{3}\right) ≈ 53.13°θ=arctan(ab​)=arctan(34​)≈53.13°

✅ Final Results:

  • Hypotenuse = 5
  • Area = 6
  • Perimeter = 12
  • Angles = 36.87° and 53.13°

🔹 Practical Applications of a Right Triangle Calculator

This tool is not only useful for students but also for many real-life applications:

  • Construction & Carpentry – Measuring walls, roof slopes, or diagonal supports.
  • Architecture – Designing buildings with accurate angles.
  • Navigation & Surveying – Calculating distances and slopes.
  • Physics & Engineering – Working with forces, vectors, and mechanics.
  • Trigonometry & Education – Helping students understand geometric principles.

🔹 Advantages of Using Our Calculator

  • Saves Time: No manual calculations.
  • Prevents Mistakes: Accurate results every time.
  • User-Friendly: Simple interface for quick use.
  • Free Access: No sign-up required.

🔹 20 Frequently Asked Questions (FAQs)

Q1. What is the formula to calculate the hypotenuse?
A: The formula is c=a2+b2c = \sqrt{a^2 + b^2}c=a2+b2​.

Q2. Can I calculate the area of a right triangle with this tool?
A: Yes, it calculates area using 12×a×b\frac{1}{2} \times a \times b21​×a×b.

Q3. Does this calculator work only for right triangles?
A: Yes, it is specifically designed for 90° right triangles.

Q4. How do I calculate perimeter?
A: By adding all three sides: a+b+ca + b + ca+b+c.

Q5. What are angles opposite legs in a right triangle?
A: They are the two acute angles formed with respect to each leg.

Q6. Can I use decimals as inputs?
A: Yes, the calculator supports decimal values.

Q7. Does the tool work on mobile devices?
A: Yes, it’s mobile-friendly.

Q8. Is there a reset button to clear values?
A: Yes, you can reset and start again anytime.

Q9. Is the calculator suitable for trigonometry problems?
A: Absolutely, it gives both side lengths and angles.

Q10. What if I enter negative values?
A: The calculator will ask for valid positive numbers.

Q11. Can I use this for physics problems involving vectors?
A: Yes, especially for force and displacement problems.

Q12. How accurate are the angle results?
A: Results are shown up to two decimal places.

Q13. Does this replace manual calculations?
A: It simplifies them but knowing formulas is still important.

Q14. What units should I use?
A: Any unit (cm, m, inches, feet) works as long as both legs use the same unit.

Q15. Can I use this for construction projects?
A: Yes, it’s useful for measuring slopes and diagonals.

Q16. Is it better than a physical calculator?
A: It’s faster because results appear instantly without multiple steps.

Q17. What is the largest angle in a right triangle?
A: Always 90°, by definition.

Q18. Can I calculate the height of a building with this tool?
A: Yes, if you know the base distance and angle of elevation.

Q19. Is the calculator free to use?
A: Yes, it’s 100% free.

Q20. Can I use it offline?
A: It works online; for offline use, you can save the page.

🔹 Final Thoughts

The 90° Triangle Calculator is a quick, reliable, and easy-to-use tool for solving right triangle problems. Whether you need the hypotenuse, area, perimeter, or angles, this calculator provides accurate results instantly.