Right Triangle Calculator Online Free
Right Triangle Calculator
Triangle Properties
Right triangle with sides a, b, c and angles α, β, and 90°
Instructions: Enter any 2 values (sides or angles) and the calculator will automatically compute all other properties. For radians, you can use expressions like π/3, π/4, π/6, etc.
A right triangle has one 90-degree angle and follows the Pythagorean theorem. This calculator finds all sides, angles, and the area when you provide any two known values. It also shows the trigonometric ratios (sin, cos, tan) for both non-right angles, making it a complete right-triangle solving tool.
Right Triangle Relationships
For a right triangle with legs a and b, hypotenuse c, and angles A and B (opposite their respective legs): Pythagorean theorem: a² + b² = c² Angles sum: A + B = 90° (since C = 90°)
sin(A) = opposite/hypotenuse = a/c cos(A) = adjacent/hypotenuse = b/c tan(A) = opposite/adjacent = a/b Inverse: A = arcsin(a/c) = arccos(b/c) = arctan(a/b)
Area = ½ × a × b (using the two legs as base and height).
SOH-CAH-TOA Reminder
The mnemonic SOH-CAH-TOA helps remember trig ratios: Sine = Opposite / Hypotenuse Cosine = Adjacent / Hypotenuse Tangent = Opposite / Adjacent These ratios are the foundation of trigonometry and are used extensively in physics, engineering, navigation, and construction.
Frequently Asked Questions
What are the two special right triangles?⌄
The 45-45-90 triangle has legs in ratio 1:1:√2. The 30-60-90 triangle has sides in ratio 1:√3:2. Memorizing these ratios speeds up many geometry calculations without needing a calculator: a 30-60-90 triangle with hypotenuse 10 has legs of 5 and 5√3 ≈ 8.66.
How do I find an angle if I know two sides?⌄
Use inverse trig functions. If you know the opposite side (a) and hypotenuse (c), angle A = arcsin(a/c). If you know both legs (a and b), angle A = arctan(a/b). Most scientific calculators have arcsin, arccos, and arctan as sin⁻¹, cos⁻¹, and tan⁻¹.
What is the relationship between the two acute angles in a right triangle?⌄
They are complementary: they always add up to 90°. If angle A = 35°, then angle B = 55°. This also means sin(A) = cos(B) and cos(A) = sin(B). The name cosine literally derives from "complement's sine."
How is the right triangle calculator used in construction?⌄
Builders use right triangle calculations constantly: calculating rafter lengths from roof rise and run, finding diagonal measurements for squaring foundations, determining cable lengths, and designing ramps with specific angles. The 3-4-5 Pythagorean triple is used to verify right angles on building layouts.