30 60 90 Special Right Triangle Calculator
Enter any known value for a 30 60 90 triangle to calculate the edge lengths, altitude, area, perimeter, inradius, and circumradius.
What is a 30 60 90 Triangle?
A 30 60 90 triangle is a special right triangle that has interior angles measuring 30°, 60°, and 90°.
You can also think of a 30 60 90 triangle as half of an equilateral triangle divided from any point to halfway along the opposite leg.
In a 30 60 90 triangle the shortest leg will be opposite the 30° angle and the longest leg, or hypotenuse, will be opposite the 90° angle.
Formulas to Solve a 30 60 90 Triangle
Because a 30 60 90 triangle is a right triangle the formulas for a right triangle can also be used on them. However, there are also a few simplified formulas that can be used on a 30 60 90 triangle as well.
Solve Leg A
Given leg b, the formula to solve leg a is:
a = b × √33
Thus, leg a is equal to leg b times the square root of 3, divided by 3.
Solve Leg B
Given leg a, the formula to solve leg b is:
b = a√3
So, leg b is equal to leg a times the square root of 3.
Calculate the Hypotenuse
In a 30 60 90 special right triangle the hypotenuse is always equal to twice the length of the shortest leg. Thus, the formula to calculate the hypotenuse c is simply c = 2a.
Find the Area
Given the side lengths of a 30 60 90 triangle, the formula to find the area is:
T = ab2
The area T is equal to leg a times leg b, divided by 2.
Like any triangle, the perimeter is equal to the sum of the edges.
p = a + b + c
So, perimeter p is simply leg a plus leg b plus hypotenuse c.
Like special right triangles? You might also like our 45 45 90 calculator.