Right Triangle Calculator 30 Degrees
'/%3E%3Ccircle cx='48' cy='39' r='19' fill='%23f2c9a5'/%3E%3Cpath d='M27 35c3-16 39-17 42 2-8-8-27-9-42-2z' fill='%23374151'/%3E%3Cpath d='M21 86c5-24 49-28 56 0z' fill='%232563eb'/%3E%3Ccircle cx='41' cy='41' r='2' fill='%23111827'/%3E%3Ccircle cx='55' cy='41' r='2' fill='%23111827'/%3E%3Cpath d='M42 52c4 3 9 3 13 0' stroke='%2392400e' stroke-width='3' fill='none' stroke-linecap='round'/%3E%3C/svg%3E)
Reviewed by Calculator Editorial Team
A right triangle with a 30-degree angle is a special right triangle that follows specific side length ratios. This calculator helps you determine the lengths of all sides when you know one side length and the angle.
What is a Right Triangle with 30 Degrees?
A right triangle with a 30-degree angle is a special case of a right triangle where one of the non-right angles is exactly 30 degrees. This creates a predictable ratio between the sides of the triangle.
The key properties of a 30-60-90 triangle are:
- The sides are in the ratio 1 : √3 : 2
- The side opposite the 30° angle is the shortest side (1)
- The side opposite the 60° angle is √3 times the shortest side
- The hypotenuse is twice the shortest side
Important Note
This calculator assumes the given angle is one of the non-right angles (either 30° or 60°). If you're working with a different type of right triangle, please use our general right triangle calculator.
How to Use the Right Triangle Calculator 30 Degrees
Using our calculator is simple:
- Select whether you know the side opposite the 30° angle or the side opposite the 60° angle
- Enter the length of the known side
- Click "Calculate" to see the results
- Review the calculated side lengths and angle measures
The calculator will display all three sides of the triangle along with the measures of all three angles.
Key Formulas for 30-Degree Right Triangles
Side Length Formulas
If you know the side opposite the 30° angle (a):
- Side opposite 60° (b) = a × √3
- Hypotenuse (c) = a × 2
If you know the side opposite the 60° angle (b):
- Side opposite 30° (a) = b / √3
- Hypotenuse (c) = b × (2/√3)
These formulas are based on the fundamental properties of 30-60-90 triangles where the sides maintain a consistent ratio.
Worked Examples
Example 1: Known Side Opposite 30°
If the side opposite the 30° angle is 5 units:
- Side opposite 60° = 5 × √3 ≈ 8.66 units
- Hypotenuse = 5 × 2 = 10 units
Example 2: Known Side Opposite 60°
If the side opposite the 60° angle is 8 units:
- Side opposite 30° = 8 / √3 ≈ 4.62 units
- Hypotenuse = 8 × (2/√3) ≈ 9.24 units
| Given Side | Opposite 30° | Opposite 60° | Hypotenuse |
|---|---|---|---|
| Opposite 30° = 5 | 5 | 8.66 | 10 |
| Opposite 60° = 8 | 4.62 | 8 | 9.24 |
Frequently Asked Questions
What is the difference between a 30-60-90 triangle and other right triangles?
A 30-60-90 triangle has specific side ratios (1 : √3 : 2) that are consistent regardless of the triangle's size. Other right triangles have different side ratios depending on their angles.
Can I use this calculator for non-right triangles?
No, this calculator is specifically designed for right triangles with a 30-degree angle. For other types of triangles, please use our general triangle calculator.
What if I know the hypotenuse instead of one of the other sides?
You can use the formulas to work backward. For example, if you know the hypotenuse (c), you can find the side opposite 30° (a) by dividing c by 2, and the side opposite 60° (b) by multiplying a by √3.
Are there any limitations to this calculator?
This calculator assumes you know either the side opposite 30° or the side opposite 60°. It doesn't account for cases where you might know other combinations of sides or angles.