Right Triangle Problem Calculator and Solver

This comprehensive problem solver helps students and teachers generate and solve various right triangle scenarios. With 11 different solving modes, you can:

📐 Create, explore, and solve custom right triangle problems

✓ Given two sides, find everything
✓ Given side and angle, find the rest
✓ Given side and area, solve the triangle
✓ Given side and perimeter, find all
✓ Given area and angle, determine sides
✓ Given perimeter and angle, solve
✓ Given hypotenuse and area
✓ Given hypotenuse and perimeter
✓ Given perimeter and area
✓ And many more combinations...

Perfect for homework help, exam preparation, or exploring geometric relationships!

The math behind the present solver is in Right Triangle Problems: Step-by-Step Solutions for 9 Different Cases

right_triangle_calculator-1.gif ( GIF image data, version 89a, 469 x 324 )

Right triangle diagram: sides a, b, hypotenuse h, and angles A, B, C

Notation

Sides: a and b are the legs (forming the right angle). h is the hypotenuse.

Angles: A is opposite side a, B is opposite side b, and C = 90°.

Relations: a² + b² = h², A + B = 90°, Area = ½ab, Perimeter = a + b + h

Right Triangle Problem Solver

Select what you know about your triangle

Step 1: Choose Your Input Mode

Select a mode from the dropdown above to see description

Step 2: Enter Your Known Values

Side a

Side b

Hypotenuse (h)

Angle A (degrees)

Perimeter (p)

Area

Decimal Places

✅ Step 3: Solution

Side Lengths

Side a --

Side b --

Hypotenuse (h) --

Angles

Angle A --°

Angle B --°

Angle C --°

Additional Properties

Area --

Perimeter --

Key Formulas Used

Pythagorean Theorem

\( a^2 + b^2 = h^2 \)

The fundamental relation for right triangles.

Trigonometric Ratios

\( \sin A = \frac{a}{h} \)
\( \cos A = \frac{b}{h} \)
\( \tan A = \frac{a}{b} \)

Area & Perimeter

\( \text{Area} = \frac{1}{2}ab \)
\( \text{Perimeter} = a + b + h \)

All 11 Solving Modes

Mode	Given	Finds	Example
Two sides	a, b	h, A, B, area, perimeter	a=3, b=4
Side & hypotenuse	a, h	b, A, B, area, perimeter	a=3, h=5
Side & angle	a, A	b, h, B, area, perimeter	a=3, A=36.87°
Hypotenuse & angle	h, A	a, b, B, area, perimeter	h=5, A=36.87°
Side & area	a, area	b, h, A, B, perimeter	a=3, area=6
Side & perimeter	a, p	b, h, A, B, area	a=3, p=12
Area & angle	area, A	a, b, h, B, perimeter	area=6, A=36.87°
Perimeter & angle	p, A	a, b, h, B, area	p=12, A=36.87°
Hypotenuse & area	h, area	a, b, A, B, perimeter	h=5, area=6
Hypotenuse & perimeter	h, p	a, b, A, B, area	h=5, p=12
Perimeter & area	p, area	a, b, h, A, B	p=12, area=6