Tangent Ratio Calculator
Calculate tangent ratios in right triangles and find angles using trigonometry
Calculate Tangent Ratio
Side opposite to the angle
Side adjacent to the angle
Longest side of the triangle
Tangent Ratio Results
Example: 3-4-5 Right Triangle
Triangle Sides
Opposite side (a): 3 units
Adjacent side (b): 4 units
Hypotenuse (c): 5 units
Tangent Calculations
For angle α: tan(α) = 3/4 = 0.75
Angle α: arctan(0.75) = 36.87°
For angle β: tan(β) = 4/3 = 1.333
Angle β: arctan(1.333) = 53.13°
Verification: 36.87° + 53.13° = 90°
Right Triangle Elements
Angle
Acute angle (0° < θ < 90°)
Opposite
Side opposite to the angle
Adjacent
Side adjacent to the angle
Hypotenuse
Longest side, opposite to 90°
Special Tangent Values
Tangent Ratio Tips
Tangent = Opposite / Adjacent
Only defined for right triangles
Range: 0 to infinity for 0° to 90°
Use arctan to find angle from ratio
Undefined at 90° (infinite slope)
Understanding the Tangent Ratio
What is the Tangent Ratio?
The tangent ratio is a fundamental trigonometric function that relates the angle in a right triangle to the ratio of the opposite side and adjacent side. It's defined as:
tan(θ) = opposite / adjacent
Key Properties
- •Domain: All real numbers except odd multiples of π/2
- •Range: All real numbers (-∞, +∞)
- •Period: π radians (180°)
- •Undefined at 90°, 270°, etc.
Applications
- •Architecture: Calculating roof slopes and ramp angles
- •Navigation: Determining angles of elevation and depression
- •Engineering: Analyzing forces and structural angles
- •Physics: Projectile motion and wave analysis
Calculation Methods
From Sides
Measure opposite and adjacent sides, then divide: tan(θ) = opp/adj
From Angle
Use calculator or table: tan(30°) = 0.577, tan(45°) = 1, etc.
Inverse Tangent
Find angle from ratio: θ = arctan(opposite/adjacent)