How do you find the hypotenuse in a 30-60-90 triangle?

The hypotenuse is found by multiplying the shortest side by 2. Formula: c = 2a.

30-60-90 Triangle Calculator

Q: What is the ratio of a 30-60-90 triangle?

The sides of a 30-60-90 triangle follow the ratio 1 : √3 : 2, where the shortest side is opposite 30°, the longest side (hypotenuse) is opposite 90°, and the middle side is opposite 60°.

Q: What is the formula for area of a 30-60-90 triangle?

The area of a 30-60-90 triangle is calculated using Area = (√3 / 2) × a², where a is the shortest side.

Q: How do you solve a 30-60-90 triangle?

You can solve a 30-60-90 triangle using the ratio 1 : √3 : 2. If one side is known, the other sides can be calculated using simple multiplication.

Q: Where are 30-60-90 triangles used?

30-60-90 triangles are used in geometry, trigonometry, engineering, architecture, construction, and RF planning because of their predictable side ratios.

Short leg (a) Long leg (b) Hypotenuse (c)

Area: 0

Perimeter: 0

Last Updated: 23-04-2026

30-60-90 Triangle Calculator

The 30-60-90 triangle calculator helps you quickly find the sides, area, and perimeter of a special right triangle whose angles are 30°, 60°, and 90°. By entering any one side, the calculator automatically computes the remaining sides using the well-known 1 : √3 : 2 ratio.

This triangle appears frequently in geometry, trigonometry, architecture, and engineering, so understanding its properties can make many math problems easier to solve.

30-60-90 Triangle Formula:
Short side = x
Long side = x√3
Hypotenuse = 2x

What Is a 30-60-90 Triangle?

A 30-60-90 triangle is a special right triangle where the three interior angles measure:

30°
60°
90°

Since it contains a right angle, the triangle follows thePythagorean theorem.

a² + b² = c²

30-60-90 Triangle Formula

A 30-60-90 triangle is a special right triangle where the side lengths always follow a fixed ratio.

1 : √3 : 2

Short leg (a) – opposite 30°
Long leg (b) = a × √3
Hypotenuse (c) = 2a

Example Calculation

If the short leg is a = 5

Step 1 – Long leg
b = a × √3 = 5 × 1.732 = 8.66

Step 2 – Hypotenuse
c = 2a = 2 × 5 = 10

Step 3 – Area
Area = ½ × a × b = ½ × 5 × 8.66 = 21.65

30-60-90 Triangle Side Ratio

The sides follow this fixed ratio:

1 : √3 : 2

Side	Description
a	Short leg (opposite 30°)
b	Long leg (opposite 60°)
c	Hypotenuse (opposite 90°)

30-60-90 triangle diagram showing 1 sqrt 3 2 ratio with labeled sides

Area and Perimeter

Area Formula

Area = ½ × a × b

Area = (√3 / 2)a²

Perimeter Formula

Perimeter = a + b + c

Perimeter = a(3 + √3)

FAQ on 30-60-90 Triangle Calculator

1. What is the ratio of a 30-60-90 triangle?

The sides of a 30-60-90 triangle always follow the fixed ratio 1 : √3 : 2, where the shortest side is opposite 30°, the longest side (hypotenuse) is opposite 90°, and the middle side is opposite 60°.

2. What is the formula for area of a 30-60-90 triangle?

The area is calculated using:
Area = (√3 / 2) × a² where a is the shortest side.

3. How do you solve a 30-60-90 triangle?

You can solve a 30-60-90 triangle by using the fixed ratio 1 : √3 : 2. If you know one side, you can calculate the other two sides using simple multiplication.

4. Where are 30-60-90 triangles used?

These triangles are widely used in geometry, trigonometry, engineering, architecture, construction, and RF planning because of their predictable side ratios.

5. How do you calculate the long leg?

The long leg (opposite 60°) is found by multiplying the short leg by √3.
Formula: b = a√3

6. Why is the ratio 1 : √3 : 2?

This ratio comes from dividing an equilateral triangle into two right triangles, which creates angles of 30°, 60°, and 90°.