Right Triangle Trigonometry Calculator

The formula

sin, cos and tan relate a right triangle’s sides and angles

SOH CAH TOA

The mnemonic covers all three ratios: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent. "Opposite" and "adjacent" are relative to the angle you are working with, which is why swapping which acute angle you use swaps sine and cosine.

What always holds

• The three angles add to 180°, without exception.
• Any two sides must add to more than the third — the triangle inequality. Sides of 4, 5 and 12 cannot close.
• The longest side always faces the largest angle.
• Area = ½ × base × height for any triangle, with the height measured perpendicular to that base.

Which formula to reach for

With three sides, use Heron’s formula. With a base and its height, use ½bh. With two sides and the angle between them, use ½ab·sin C. With a right angle, the two legs are already base and height, so the area is just half their product.