Triangle Ratio Calculator
Calculate triangle angles from ratios or find angle ratios from given angles
Triangle Ratio Calculator
Angle Ratio (x : y : z)
Enter the ratio components. For example, for ratio 2:3:4, enter x=2, y=3, z=4
Example Calculations
Example 1: Ratio 2:3:4
Given ratio: 2:3:4
Step 1: Find x = 180° ÷ (2+3+4) = 180° ÷ 9 = 20°
Step 2: Calculate angles:
• α = 2 × 20° = 40°
• β = 3 × 20° = 60°
• γ = 4 × 20° = 80°
Result: Angles are 40°, 60°, 80°
Example 2: Right Triangle 1:1:2
Given ratio: 1:1:2
Step 1: Find x = 180° ÷ (1+1+2) = 180° ÷ 4 = 45°
Step 2: Calculate angles: 45°, 45°, 90°
Result: This is a right isosceles triangle!
Common Triangle Ratios
1:2:3 (30-60-90)
Angles: 30°, 60°, 90°
Right triangle with special properties
1:1:2 (45-45-90)
Angles: 45°, 45°, 90°
Right isosceles triangle
1:1:1 (60-60-60)
Angles: 60°, 60°, 60°
Equilateral triangle
3:4:5
Angles: 45°, 60°, 75°
Scalene triangle
Key Formulas
Angle Sum
α + β + γ = 180°
Ratio to Angles
x = 180° ÷ (a + b + c)
Law of Sines
a/sin(α) = b/sin(β) = c/sin(γ)
Ratio Simplification
Divide by GCD of all terms
Understanding Triangle Ratios
What are Triangle Ratios?
Triangle ratios express the relationship between angles in a triangle. If angles are in the ratio a:b:c, we can write them as ax, bx, and cx, where x is a constant. Since angles in a triangle sum to 180°, we can solve for x and find all angles.
Applications
- •Finding missing angles when ratio is known
- •Simplifying angle relationships
- •Identifying special triangles
- •Solving geometry problems
Step-by-Step Method
Given ratio a:b:c
1. Write angles as ax, bx, cx
2. Use: ax + bx + cx = 180°
3. Simplify: (a + b + c)x = 180°
4. Solve: x = 180° ÷ (a + b + c)
5. Calculate: α = ax, β = bx, γ = cx
Note: This method works because the sum of angles in any triangle is always 180°, a fundamental property of Euclidean geometry.