Right Triangle Calculator

Right triangle calculator calculates the side length, angle, area, or perimeter from another known side or angle for a right triangle.

A right triangle is a triangle with one angle that is 90°(also called the right angle). The two sides of the right angle are the leg, and the opposite side of the right angle is the hypotenuse.
The area formula for a right triangle is:
A = (a x b)/2
(a and b are both legs for the right triangle)
The perimeter formula for a right triangle is adding all the sides together.
P=a+b+c.

Find hypotenuse of a right triangle

To find hypotenuse c by giving two legs:
c=√(a²+b²)
To find hypotenuse by giving a leg and an angle, we need to apply the law of sin formula which is:
^a⁄_sin(X)=^b⁄_sin(Y)=^c⁄_sin(90°)
(sin90°=1)
Therefore
c= ^a⁄_sin(X) OR
c=^b⁄_sin(Y)

Find the side of a right triangle

To find a leg by known leg and hypotenuse
a = c²-b² OR
b =c²-a²
By known hypotenuse and an angle.
a=c x sin(X).
b=c x sin(Y)

Find the angle of a right triangle

There are multiway to find an angle of a right triangle.
by known two other sides (either legs or hypotenuse).
To find angle X:
X=sin^-1(a/c)
X=cos^-1(b/c)
X=tan^-1(a/b)
X=cot^-1(b/a)
To find angle Y:
Y=sin^-1(b/c)
Y=cos^-1(a/c)
Y=tan^-1(b/a)
Y=cot^-1(a/b)
By known the other angle:
X=90°-Y OR Y=90°-X
(because a triangle is 180° for 3 angles altogether, the right angle is 90°, and the other two angles are 180-90=90°)