Right Triangle Trigonometry Calculator
Calculate all properties of right triangles using trigonometric functions and relationships
Triangle Properties
Sides
Angles
Other Properties
Example Calculation
Given: Hypotenuse c = 5, Angle A = 38°
Step 1: Calculate angle B = 90° - 38° = 52°
Step 2: Calculate opposite side: a = c × sin(A) = 5 × sin(38°) = 5 × 0.6157 = 3.078
Step 3: Calculate adjacent side: b = c × cos(A) = 5 × cos(38°) = 5 × 0.7880 = 3.940
Step 4: Calculate area: Area = (a × b)/2 = (3.078 × 3.940)/2 = 6.063
Trigonometric Functions
Sine (sin)
sin(A) = opposite/hypotenuse
Ratio of opposite side to hypotenuse
Cosine (cos)
cos(A) = adjacent/hypotenuse
Ratio of adjacent side to hypotenuse
Tangent (tan)
tan(A) = opposite/adjacent
Ratio of opposite to adjacent side
Quick Tips
In a right triangle, one angle is always 90°
The sum of all angles equals 180°
Pythagorean theorem: a² + b² = c²
SOH-CAH-TOA helps remember trig ratios
Any two values can solve the triangle
Understanding Right Triangle Trigonometry
What is Right Triangle Trigonometry?
Right triangle trigonometry relates the angles of a right triangle to the lengths of its sides. The three primary trigonometric functions (sine, cosine, and tangent) provide the foundation for solving any right triangle when given at least two pieces of information.
Key Relationships
- •Pythagorean Theorem: a² + b² = c²
- •Complementary Angles: A + B = 90°
- •Area Formula: Area = (a × b)/2
- •Co-function Identities: sin(A) = cos(B)
Solving Methods
Given Two Sides
Use Pythagorean theorem to find the third side, then trigonometric ratios for angles.
Given One Angle and One Side
Use trigonometric functions and their inverses to find remaining sides and angles.
Given Area and One Side
Use area formula A = ½ab to find the other leg, then proceed normally.