Right Triangle Calculator
SOH-CAH-TOA and the Pythagorean theorem solve any right triangle: legs 3 and 4 give hypotenuse 5 and angles 36.87° and 53.13°.
5
- Leg a
- 3
- Leg b
- 4
- Angle A (opposite a)
- 36.86989765 °
- Angle B (opposite b)
- 53.13010235 °
- sin A = a/c
- 0.6
- cos A = b/c
- 0.8
- tan A = a/b
- 0.75
- Area
- 6
- Perimeter
- 12
Step-by-step solution
- SOH-CAH-TOA: sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent
- a = 3, b = 4, c = √(a² + b²) = 5
- A = tan⁻¹(a/b) = 36.86989765°, B = 90° − A = 53.13010235°
Right Triangle Formula
sin A = a/c, cos A = b/c, tan A = a/b
SOH-CAH-TOA; A + B = 90°
Worked Example
A right triangle with legs 3 and 4:
- SOH-CAH-TOA: sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent
- a = 3, b = 4, c = √(a² + b²) = 5
- A = tan⁻¹(a/b) = 36.86989765°, B = 90° − A = 53.13010235°
Leg b: 4 · Angle A (opposite a): 36.86989765 ° · Angle B (opposite b): 53.13010235 ° · sin A = a/c: 0.6 · cos A = b/c: 0.8 · tan A = a/b: 0.75 · Area: 6 · Perimeter: 12
Test-day tip
Set the SAT graphing calculator to degrees before using trig functions; a radian setting is the most common cause of wrong answers in trig questions.
More Geometry and Trigonometry Calculators
-
Special Right Triangles Calculator
30-60-90: 1 : √3 : 2; 45-45-90: 1 : 1 : √2
short leg : long leg : hypotenuse; leg : leg : hypotenuse
Example: A 30-60-90 triangle with short leg 5: Sides: short leg = 5, long leg = 5√3, hypotenuse = 10.
-
Pythagorean Theorem Calculator
a² + b² = c²
c hypotenuse (opposite the right angle), a and b legs
Example: A right triangle with legs 6 and 8: Hypotenuse c = 10.
-
Distance Formula Calculator
d = √[(x₂ − x₁)² + (y₂ − y₁)²]
the Pythagorean theorem on the coordinate plane
Example: The points (1, 2) and (7, 10): Distance d = 10.
-
Midpoint Calculator
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
endpoint: x₂ = 2Mx − x₁, y₂ = 2My − y₁
Example: The segment from (−2, 3) to (6, −5): Midpoint = (2, -1).
Frequently asked questions
Why is sin A = cos B in a right triangle?
A and B are complementary (they add to 90°), and the side opposite A is adjacent to B. The SAT tests sin x° = cos(90 − x)° often.
How do I find an angle from two sides?
Use the inverse trig function matching the sides: A = tan⁻¹(opposite/adjacent), sin⁻¹(opposite/hypotenuse) or cos⁻¹(adjacent/hypotenuse).
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Right Triangle Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/right-triangle-calculator/
IEEE
Scientific Converters, "Right Triangle Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/right-triangle-calculator/