Right Triangle Calculator
Based on Pythagorean Theorem ($a^2 + b^2 = c^2$) to calculate the hypotenuse.
What is a Right Triangle?
A triangle where one angle is 90ยฐ. The longest side opposite to 90ยฐ is called the hypotenuse (b), and the other two sides are the base (a) and height (h).
Pythagorean Theorem
bยฒ = aยฒ + hยฒ
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
When base (a) and height (h) are known
b = โ(aยฒ + hยฒ)
ฮธ = arctan(h / a)
S = (1/2) ร a ร h
When base (a) and hypotenuse (b) are known
ฮธ = arccos(a / b)
h = a ร tan(ฮธ)
S = (1/2) ร a ร h
When base (a) and angle (ฮธ) are known
b = a / cos(ฮธ)
h = a ร tan(ฮธ)
S = (1/2) ร a ร h
When hypotenuse (b) and height (h) are known
ฮธ = arcsin(h / b)
a = b ร cos(ฮธ)
S = (1/2) ร a ร h
Congruence Conditions for Right Triangles
RHA: Hypotenuse and one acute angle are equal
RHS: Hypotenuse and another side are equal
Special Angle Ratios
30ยฐ-60ยฐ-90ยฐ โ side ratio: 1 : โ3 : 2
45ยฐ-45ยฐ-90ยฐ โ side ratio: 1 : 1 : โ2