Our Right Triangle Solver helps you quickly find the unknown sides and angles of any right-angled triangle. Just enter any two known values (sides or angles, excluding the 90° angle) and let the calculator do the rest. Ideal for geometry homework and trigonometry problems.
Length of the side opposite Angle A
Length of the side opposite Angle B
Length of the hypotenuse (opposite the 90° angle)
Measure of Angle A in degrees
Measure of Angle B in degrees
Our Right Triangle Solver helps you quickly find the unknown sides and angles of any right-angled triangle. Just enter any two known values (sides or angles, excluding the 90° angle) and let the calculator do the rest. Ideal for geometry homework and trigonometry problems.
In a right-angled triangle, with angle C = 90°: Pythagorean Theorem: a² + b² = c² Trigonometric Ratios (SOH CAH TOA): sin(A) = a/c cos(A) = b/c tan(A) = a/b sin(B) = b/c cos(B) = a/c tan(B) = b/a Angle Sum: A + B = 90°
Imagine a right triangle where side 'a' (opposite Angle A) is 3 units and side 'b' (opposite Angle B) is 4 units. We want to find the hypotenuse 'c', Angle A, and Angle B. Using the Pythagorean theorem: c² = 3² + 4² = 9 + 16 = 25, so c = 5. Using trigonometry: Angle A = arctan(a/b) = arctan(3/4) ≈ 36.87° Angle B = arctan(b/a) = arctan(4/3) ≈ 53.13° Check: 36.87° + 53.13° = 90°.
A right triangle is a triangle that has one angle measuring exactly 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse, and it's always the longest side of the triangle.
To solve a right triangle, you typically need at least two pieces of information, besides the inherent 90-degree angle. This could be two sides, or one side and one acute angle (an angle less than 90 degrees). Our calculator will then find all the other missing sides and angles.
The solver uses fundamental geometric principles and trigonometry. It applies the Pythagorean theorem (a² + b² = c²) for finding sides and trigonometric ratios (SOH CAH TOA: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent) to determine angles and sides.
No, this specific solver is designed only for right-angled triangles. For other types of triangles (like acute or obtuse triangles), you would typically use the Law of Sines or the Law of Cosines, which are different formulas.
Right-angled triangles are fundamental building blocks in geometry and trigonometry, appearing everywhere from construction to navigation. Whether you're tackling homework or a real-world problem, knowing how to find missing sides and angles is a crucial skill. This guide will walk you through the principles of solving right triangles and show you how to use our online Right Triangle Solver to make calculations quick and accurate.
A right triangle is defined by having one angle that measures exactly 90 degrees. The side opposite this right angle is called the hypotenuse, which is always the longest side. The other two sides are often referred to as legs. To solve a right triangle means to find the lengths of all its sides and the measures of all its angles, given some initial information. The key tools for solving right triangles are the Pythagorean theorem and the basic trigonometric ratios (SOH CAH TOA). The Pythagorean theorem relates the lengths of the three sides, while SOH CAH TOA connects angles to the ratios of side lengths. By combining these, you can determine any unknown value as long as you have at least two pieces of information (excluding the 90-degree angle itself).
For a right-angled triangle with angles A, B, C (where C = 90°) and opposite sides a, b, c (where c is the hypotenuse): 1. **Pythagorean Theorem:** a² + b² = c² 2. **Angle Sum Property:** A + B = 90° 3. **Trigonometric Ratios (SOH CAH TOA):** * **SOH:** Sine(Angle) = Opposite / Hypotenuse sin(A) = a / c sin(B) = b / c * **CAH:** Cosine(Angle) = Adjacent / Hypotenuse cos(A) = b / c cos(B) = a / c * **TOA:** Tangent(Angle) = Opposite / Adjacent tan(A) = a / b tan(B) = b / a
Let's work through an example. Suppose you have a right triangle where side 'a' is 6 units long and Angle A is 30 degrees. We need to find side 'b', side 'c' (hypotenuse), and Angle B. 1. **Find Angle B:** Since A + B = 90°, B = 90° - 30° = 60°. 2. **Find Hypotenuse 'c' (using sin A):** sin(A) = a / c sin(30°) = 6 / c 0.5 = 6 / c c = 6 / 0.5 = 12 units. 3. **Find Side 'b' (using tan A):** tan(A) = a / b tan(30°) = 6 / b 0.5774 ≈ 6 / b b ≈ 6 / 0.5774 ≈ 10.39 units. So, the missing values are side b ≈ 10.39, side c = 12, and Angle B = 60°.
Using the ProMathTools Right Triangle Solver is straightforward. Simply input the two known values into the corresponding fields. For example, if you know two sides, enter their lengths into 'Side a', 'Side b', or 'Side c'. If you know one side and one angle, enter those values. The calculator will automatically determine the remaining sides and angles. Remember to leave the fields for unknown values blank. The results will be displayed with high precision, giving you all the properties of your right triangle.
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