Angle of Right Triangle Calculator
Calculate the angles of a right triangle using sides or area measurements
Calculate Right Triangle Angles
Length of the side opposite to angle α
Length of the side opposite to angle β
Length of the hypotenuse (longest side)
Use with one side to find the other side
❌ Please enter at least two values (sides or area with one side)
Example Calculation
Example: 3-4-5 Triangle
Given: Side a = 3, Side b = 4
Step 1: Calculate hypotenuse: c = √(3² + 4²) = √(9 + 16) = 5
Step 2: Calculate angle α: α = arctan(3/4) = 36.87°
Step 3: Calculate angle β: β = 90° - 36.87° = 53.13°
Result
Angles: α = 36.87°, β = 53.13°, γ = 90°
Verification: 36.87° + 53.13° + 90° = 180° ✓
Trigonometric Functions
Sine (sin)
sin(α) = opposite/hypotenuse = a/c
Cosine (cos)
cos(α) = adjacent/hypotenuse = b/c
Tangent (tan)
tan(α) = opposite/adjacent = a/b
Right Triangle Properties
One angle is always 90°
The other two angles are complementary (sum to 90°)
Follows Pythagorean theorem: c² = a² + b²
Hypotenuse is the longest side
Area = (1/2) × base × height
Understanding Right Triangle Angles
What is a Right Triangle?
A right triangle is a triangle with one angle measuring exactly 90 degrees. The other two angles are acute angles that together sum to 90 degrees, making them complementary angles.
Finding the Angles
- •If you know two sides, use trigonometric functions
- •If you know one angle, subtract from 90° to find the other
- •Use area and one side to find the other side first
Inverse Trigonometric Functions
- arcsin(x): Inverse sine function
- arccos(x): Inverse cosine function
- arctan(x): Inverse tangent function
Common Applications
- • Architecture and construction
- • Engineering calculations
- • Navigation and surveying
- • Physics problems
- • Computer graphics