Matemáticas y Álgebra

Trigonometry & Right Triangle Solver — sin, cos, tan & SVG Visualizer

Trigonometry connects geometry and algebra by analyzing relationships between triangle sides and angles. Our free Trigonometry Calculator solves right-angled triangles instantly when given any two known values (sides or angles). Compute hypotenuse length, opposite and adjacent sides, internal angles, triangle area, and perimeter alongside an interactive SVG right triangle diagram. It also evaluates all six trigonometric ratios (sin, cos, tan, csc, sec, cot) in both degrees and radians.

Trigonometry & Right Triangle Solver

Solve right triangle sides/angles & evaluate sin, cos, tan, cot, sec, csc

Enter any 2 known values (e.g., Side a & Side b, or Side a & Hypotenuse c, or Side a & Angle A) to solve the triangle:

Side a (Opposite)

Side b (Adjacent)

Hypotenuse c

Angle A (°)

Solved Triangle Dimensions

Side a (Opposite):

3.0000

Side b (Adjacent):

4.0000

Hypotenuse c:

5.0000

Angle A (α):

36.87°

Angle B (β):

53.13°

Area / Perimeter:

Area: 6.00 | P: 12.00

Interactive Triangle Diagram

Mathematical Formulas & Calculation Methods

SOH CAH TOA Trig Ratios

Basic right triangle ratios for angle A.

sin(A) = opp / hyp | cos(A) = adj / hyp | tan(A) = opp / adj

Pythagorean Theorem

Relates the hypotenuse c to leg sides a and b.

a² + b² = c² ⇒ c = √(a² + b²)

Reciprocal Trig Functions

Ratios inverse to sine, cosine, and tangent.

csc(A) = hyp / opp | sec(A) = hyp / adj | cot(A) = adj / opp

Degree to Radian Conversion

Converts angle units.

Radians = Degrees × (π / 180) | Degrees = Radians × (180 / π)

Worked Step-by-Step Examples

Example 1: Solving Right Triangle with Legs a=6 and b=8

"Find hypotenuse c and angle A for right triangle with legs a=6, b=8."

Steps:

Apply Pythagorean theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.
Calculate angle A using arctan: A = arctan(opposite/adjacent) = arctan(6/8) = arctan(0.75).
Convert arctan to degrees: A ≈ 36.87°.
Calculate angle B: B = 90° - 36.87° = 53.13°.

Result: Hypotenuse c = 10, Angle A = 36.87°, Angle B = 53.13°

Example 2: Evaluating Trig Functions for 45° Angle

"Find sin(45°), cos(45°), and tan(45°)."

Steps:

sin(45°) = 1/√2 = √2/2 ≈ 0.7071.
cos(45°) = 1/√2 = √2/2 ≈ 0.7071.
tan(45°) = sin(45°)/cos(45°) = 1.

Result: sin(45°) ≈ 0.7071, cos(45°) ≈ 0.7071, tan(45°) = 1

What is Solucionador de Trigonometry & Right Triangle?

A trigonometry calculator is a geometric solver that computes side lengths, angles, and trigonometric ratio values for right-angled triangles. Trigonometry stems from the Greek words 'trigonon' (triangle) and 'metron' (measure).

Right triangles contain one 90-degree angle. The side opposite the right angle is called the hypotenuse, which is always the longest side. The remaining two sides are designated as opposite or adjacent relative to whichever acute reference angle is being evaluated.

Trigonometric functions extend beyond triangles into physics wave mechanics, harmonic motion, alternating current (AC) electricity, signal processing, spatial navigation, and computer graphics shaders.

How to Use Solucionador de Trigonometry & Right Triangle

1Enter any 2 known values (e.g. Side a and Side b, or Side c and Angle A).
2Toggle your preferred angle unit: Degrees (deg) or Radians (rad).
3Click Calculate to view all remaining sides, angles, perimeter, area, and trig function values.
4Observe the generated SVG right triangle graphic to visually verify side and angle proportions.

Key Features

Complete right triangle side and angle solver.
Evaluates all 6 trigonometric ratios (sin, cos, tan, csc, sec, cot).
Inverse trig function calculator (arcsin, arccos, arctan).
Degree and Radian angle unit converter.
Dynamic SVG right triangle diagram generator.

Benefits of Using Solucionador de Trigonometry & Right Triangle

Eliminates manual trigonometric table lookups.

Provides instant visualization of right triangle dimensions.

Helps physics students resolve force vectors into x and y components.

Prevents degree vs radian calculation errors on homework.

Practical Use Cases

High School & College Physics Students

Resolve velocity vectors, incline plane forces, and trajectory angles.

Geometry Students

Solve right triangle homework problems and check inverse trig calculations.

Carpenters & Builders

Calculate roof pitch angles, stair rise/run lengths, and corner squareness.

Surveyors & Navigators

Determine elevation heights, distance across rivers, and compass bearings.

Frequently Asked Questions

What does SOH CAH TOA mean?

SOH CAH TOA is a memory aid for right triangle trig ratios: SOH = Sin(Angle) = Opposite / Hypotenuse; CAH = Cos(Angle) = Adjacent / Hypotenuse; TOA = Tan(Angle) = Opposite / Adjacent.

How many known values do I need to solve a right triangle?

You need at least 2 known values, with at least one being a side length (e.g., 2 sides, or 1 side + 1 acute angle). Knowing only angles is insufficient because triangles can be scaled to any size.

What is the difference between degrees and radians?

Degrees divide a full circle into 360 equal parts. Radians measure angles based on arc length along a unit circle (a full circle equals 2π radians ≈ 6.28318 rad).

What are inverse trigonometric functions?

Inverse trig functions (arcsin, arccos, arctan) take a ratio of side lengths as input and return the corresponding angle in degrees or radians.

How do you find the hypotenuse of a right triangle?

Use the Pythagorean theorem: c = √(a² + b²), where a and b are the lengths of the two legs adjacent to the right angle.

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