Right Triangle Calculator – Free Online Calculator

Last Updated : 18 Apr, 2024

Right Triangle Calculator: A tool designed to solve problems related to right triangles. A right triangle is a type of triangle where one angle is exactly 90 degrees. This GeeksforGeeks tool is incredibly helpful in fields like geometry, construction, and navigation, where precise measurements are crucial. Whether you’re a student dealing with math homework or a professional needing accurate calculations, the right triangle calculator makes it easier to get fast and accurate results.

How to Use the Right Triangle Calculator

Calculating the sides and angles of a right triangle can be done using the following steps:

1. Identify Known Values: Begin by identifying which sides or angles you already know. In a right triangle, you will typically know at least one side and one other value (side or angle).

2. Use Trigonometric Ratios: Utilize the sine (sin), cosine (cos), and tangent (tan) functions to relate the angles and sides. For instance,

sin(angle) = opposite/hypotenuse,
cos(angle) = adjacent/hypotenuse
tan(angle) = opposite/adjacent.

3. Apply the Pythagorean Theorem: If you have the lengths of two sides and need to find the third, use the Pythagorean Theorem (a² + b² = c²), where ‘c’ is the hypotenuse and ‘a’ and ‘b’ are the legs of the triangle.

What is a Right Triangle Calculator?

A right triangle calculator is a tool that shows you how to calculate the missing sides and angles of a right triangle without the need for digital tools or software. It’s a method based on the principles of trigonometry and geometry that you can apply using simple mathematical operations.

Right Triangle Calculator Formula

The Right Triangle Calculator formula is a set of mathematical rules used to calculate the lengths of sides and angles in a right triangle. Here are the key components:

1. Pythagorean Theorem: This is the most famous formula associated with right triangles. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The formula is: (a² + b² = c²)

2. Trigonometric Ratios: These are used to find the angles of a right triangle when the lengths of the sides are known.

Sine (sin): This ratio is the opposite side divided by the hypotenuse.
Cosine (cos): This ratio is the adjacent side divided by the hypotenuse.
Tangent (tan): This ratio is the opposite side divided by the adjacent side.

Right Triangle Calculator Table

Here’s a table for a right triangle calculator with arbitrary values:

Known Values	Calculation	Result
Side ‘a’ = 3	Use trigonometric ratios: sin(A) = a / c, cos(A) = b / c, tan(A) = a / b	Angle ‘A’ ≈ 36.87°
Side ‘b’ = 4	Use trigonometric ratios: sin(B) = b / c, cos(B) = a / c, tan(B) = b / a	Angle ‘B’ ≈ 53.13°
Angle ‘C’ = 45°	Use trigonometric ratios: sin(C) = a / c, cos(C) = b / c, tan(C) = a / b	Side ‘c’ ≈ 5.66
Side ‘a’ = 6	Apply the Pythagorean Theorem: c = sqrt(a^2 + b^2)	Side ‘c’ ≈ 7.81
Side ‘b’ = 8	Apply the Pythagorean Theorem: c = sqrt(a^2 + b^2)	Side ‘c’ ≈ 10
Side ‘c’ = 10	Use trigonometric ratios: a = c * sin(C), b = c * cos(C)	Side ‘a’ ≈ 7.07, Side ‘b’ ≈ 7.07
Angle ‘C’ = 60°	Use trigonometric ratios: a = c * sin(C), b = c * cos(C)	Side ‘a’ ≈ 5, Side ‘b’ ≈ 8.66

Solved Examples on Right Triangle Calculator

1. Given a right triangle with legs of 6 units and 8 units, find the hypotenuse and angles.

Hypotenuse (c) = √(6² + 8²) = √(36 + 64) = √100 = 10 units.

Angle (A) = tan⁻¹(6/8) = tan⁻¹(0.75) ≈ 36.87 degrees

2. Given a right triangle with one leg of 7 units and a hypotenuse of 25 units, find the other leg and angles.

leg (b) = √(25² – 7²) = √(625 – 49) = √576 = 24 units.

Angle (A) = sin⁻¹(7/25) = sin⁻¹(0.28) ≈ 16.26 degrees.

3. Given a right triangle with one angle of 30 degrees and an adjacent leg of 10 units, find the opposite leg and hypotenuse.

Opposite leg (a) = tan(30 degrees) × 10 ≈ 5.77 units.

Hypotenuse (c) = 10 / cos(30 degrees) ≈ 11.55 units.

3 Practice Questions on Right Triangle Calculator

1. What is the length of the hypotenuse in a right triangle with legs of 9 units and 12 units?

2. If one angle of a right triangle is 45 degrees and the adjacent leg is 5 units, what is the length of the hypotenuse?

3. Find the length of the opposite leg in a right triangle with an angle of 60 degrees and an adjacent leg of 8 units.

Conclusion

Right triangle calculator is a powerful tool for anyone needing to solve problems related to right triangles. It helps you quickly find the lengths of sides and angles, making it easier to understand and apply the principles of trigonometry. By using right triangle calculator, you can save time and ensure accuracy in your calculations, enhancing your learning or professional tasks.