Hypotenuse Calculator

Understanding Hypotenuse

In a right-angled triangle, the hypotenuse is the longest side, opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This is expressed as the formula: $$a^2 + b^2 = c^2$$. Alternatively, if you know one side and an acute angle (not the right angle), trigonometric ratios like sine and cosine can be used to calculate the hypotenuse. For example, if you know the adjacent side and the angle, you can use the formula: $$ Hypotenuse = \frac{Adjacent}{cos(\theta)} $$. If you know the opposite side and the angle, use: $$ Hypotenuse = \frac{Opposite}{sin(\theta)} $$. This calculator helps you find the hypotenuse using these methods.