Quiz: Right Triangle Side and Angle Calculator
Try our right triangle calculator quiz to test your knowledge of the Pythagorean theorem, trigonometric ratios, and area formulas!
Hypotenuse10
Opposite side5
Adjacent side8.660254
Angles30°, 60°, 90°
Area21.650635
Perimeter23.660254
The ratios
| sin 30° | opposite ÷ hypotenuse = 0.5 |
| cos 30° | adjacent ÷ hypotenuse = 0.866025 |
| tan 30° | opposite ÷ adjacent = 0.57735 |
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 × heightfor 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.