Right Triangle Side and Angle Calculator
Finding out the missing side or angle couldn't be easier than with our great tool  right triangle side and angle calculator. Choose two given values, type them into the calculator and the remaining unknowns will be determined in a blink of an eye! If you are wondering how to find the missing side of a right triangle, keep scrolling and you'll find the formulas behind our calculator.
How to find the sides of a right triangle
There are a few methods of obtaining right triangle side lengths. Depending on what is given, you can use different relationships or laws to find the missing side:
 Given two sides
If you know two other sides of the right triangle, it's the easiest option; all you need to do is apply the Pythagorean theorem:
a² + b² = c²

if leg
a
is the missing side, then transform the equation to the form when a is on one side, and take a square root:a = √(c²  b²)

if leg
b
is unknown, thenb = √(c²  a²)

for hypotenuse c missing, the formula is
c = √(a² + b)²
 Given angle and hypotenuse
Apply the law of sines or trigonometry to find the right triangle side lengths:

a = c * sin(α)
ora = c * cos(β)

b = c * sin(β)
orb = c * cos(α)
 Given angle and one leg
Find the missing leg using trigonometric functions:

a = b * tan(α)

b = a * tan(β)
 Given area and one leg
As we remember from basic triangle area formula, we can calculate the area by multiplying triangle height and base and dividing the result by two. A right triangle is a special case of a scalene triangle, in which one leg is the height when the second leg is the base, so the equation gets simplified to:
area = a * b / 2
For example, if we know only the right triangle area and the length of the leg a
, we can derive the equation for other sides:
b = 2 * area / a
c = √(a² + (2 * area / a)²)
How to find the angle of a right triangle
If you know one angle apart from the right angle, calculation of the third one is a piece of cake:
Givenβ
: α = 90  β
Givenα
: β = 90  α
However, if only two sides of a triangle are given, finding the angles of a right triangle requires applying some basic trigonometric functions:
for α
sin(α) = a / c
soα = arcsin(a / c)
(inverse sine)cos(α) = b / c
soα = arctan(b / c)
(inverse cosine)tan(α) = a / b
soα = arctan(a / b)
(inverse tangent)cot(α) = b / a
soα = arctan(b / a)
(inverse cotangent)
and for β
sin(β) = b / c
soα = arcsin(b / c)
(inverse sine)cos(β) = a / c
soα = arctan(a / c)
(inverse cosine)tan(β) = b / a
soα = arctan(b / a)
(inverse tangent)cot(β) = a / b
soα = arctan(a / b)
(inverse cotangent)
How to find the missing side of a right triangle? How to find the angle? Example
Let's show how to find the sides of a right triangle with this tool:
 Assume we want to find the missing side given area and one side. Select the proper option from a dropdown list. It's the third one.
 Type in the given values. For example, an area of a right triangle is equal to 28 in² and b = 9 in.
 Our right triangle side and angle calculator displays missing sides and angles! Now we know that:
 a = 6.222 in
 c = 10.941 in
 α = 34.66°
 β = 55.34°