Online Calculators > Math Calculators > Right Triangle Calculator

# Right Triangle Calculator

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

## Right Angle Triangle Calculator

Known
Leg a
Leg b
Hypotenuse c
Angle X ° (in Degree)
Angle Y ° (in Degree)
 Results Hypotenuse c 43.01 Leg a Leg b Angle X 35.54° Angle Y 54.46° Area 437.5 Perimeter 103.01

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:
asin(X)=bsin(Y)=csin(90°)
(sin90°=1)
Therefore
c= asin(X) OR
c=bsin(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°)

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