Right Triangle Calculator

About

Fill in any two of a right triangle's sides and angles, with at least one side, and the rest is worked out: both legs, the hypotenuse, both angles, the area, the perimeter and the height onto the hypotenuse. The triangle is drawn to scale and each answer comes with its working underneath.

What do sin, cos and tan mean here?

For angle A, sin is the opposite side over the hypotenuse, cos is the adjacent side over the hypotenuse, and tan is opposite over adjacent. That is how a side and an angle give you the other sides: with a = 10 and A = 30 degrees, c = a / sin A = 20.

Which side is which?

The right angle is at corner C. Side a is opposite angle A, side b is opposite angle B, and c is the hypotenuse, the long side across from the right angle. On the drawing a runs along the bottom and b up the left.

Why can't I solve it from two angles?

In a right triangle the angles are 90 degrees plus two that add to 90, so one angle gives you the other. Both together say nothing about size: a 3-4-5 triangle and a 30-40-50 triangle have the same angles. Add one side.

What if I fill in three boxes?

The two you edited last are used and the third is solved instead, so you can change a value without clearing the others first.

Why does it say the hypotenuse must be longer?

The hypotenuse is always the longest side. If a leg is as long as or longer than c, no right triangle fits, because the other leg would have to be zero or imaginary.

How do I find a roof pitch or a ramp angle?

Put the rise in one leg and the run in the other: a = 4 and b = 12 gives A = 18.4349 degrees, which is a 4-in-12 pitch. For a ramp, rise and length (the hypotenuse) give the angle the same way.